Gr 10 Math Ch 10 SUM: Measurement

What happens to the volume of a rectangular prism when all three dimensions are multiplied by 5?

The volume is multiplied by 15.
The volume remains the same.
The volume is multiplied by 125. (correct)
The volume is multiplied by 25.

When only the height of a cylinder is multiplied by a factor of k, how does this affect the volume?

The volume is multiplied by k. (correct)
The volume remains the same.
The volume is multiplied by $k^2$.
The volume is multiplied by $k^3$.

What is the effect on the surface area of a rectangular prism if one dimension is multiplied by k?

The surface area is multiplied by $k^2$. (correct)
The surface area is unchanged.
The surface area is multiplied by $k^3$.
The surface area is multiplied by k.

If two dimensions of a rectangular prism are multiplied by 5, how does the surface area change?

The surface area is multiplied by 25. (A) Signup and view all the answers

What is the formula for the volume of a right cone?

$rac{1}{3} imes ext{Area of base} imes ext{Height of cone}$ (D) Signup and view all the answers

Which of the following accurately describes the change in volume when the radius of a cylinder is multiplied by k?

The volume is multiplied by $k^2$. (B) Signup and view all the answers

How does the surface area of a pyramid change when its dimensions are multiplied by a factor of $k$?

It increases by a factor of $k^2$ (A) Signup and view all the answers

When a rectangular prism has one dimension multiplied by k, how is the surface area affected?

The surface area is multiplied by a factor that includes k. (A) Signup and view all the answers

What is the formula used to calculate the volume of a triangular pyramid?

$rac{1}{3} imes rac{1}{2} b h imes H$ (C) Signup and view all the answers

If all dimensions of a cylinder are multiplied by k, how does the surface area change?

The surface area is multiplied by $k^2$. (B) Signup and view all the answers

Multiply the height of a cylinder by k. What effect does this have on the surface area?

The surface area is multiplied by k. (C) Signup and view all the answers

Which of the following describes a right pyramid?

A solid with polygonal base and an apex directly above the center of the base (D) Signup and view all the answers

What is the surface area formula for a right cone?

$ ext{Area of base} + ext{Area of walls}$ (B) Signup and view all the answers

What is the formula for the volume of a sphere?

$rac{4}{3} ext{Volume} = au r^3$ (D) Signup and view all the answers

Which of the following correctly states the relationship between the volume and surface area when dimensions are scaled by a factor of $k$?

Surface area changes by $k^2$ and volume by $k^3$ (A) Signup and view all the answers

What is the correct surface area formula for a square pyramid?

$b^2 + 4 imes rac{1}{2} b h_s$ (C) Signup and view all the answers

What is the formula for calculating the area of a trapezium?

A = ½ × (a + b) × h (C) Signup and view all the answers

Which of the following shapes has the same formula for area as a rectangle?

Parallelogram (B) Signup and view all the answers

How is the surface area of a triangular prism calculated?

Area of two triangles and three rectangles (A) Signup and view all the answers

What defines a right prism?

The vertical faces are perpendicular to the base (A) Signup and view all the answers

What is a key characteristic of the volume of a cylinder?

It is calculated using πr² times the height (A) Signup and view all the answers

Which formula is used to calculate the area of a circle?

A = πr² (D) Signup and view all the answers

What does the surface area of a cube consist of?

Six identical squares (A) Signup and view all the answers

Which of the following shapes does NOT belong to the category of right prisms?

Pyramid (D) Signup and view all the answers

What is the formula used to calculate the area of a triangle?

$A = ½ × b × h$ (C) Signup and view all the answers

Which statement correctly describes a right prism?

A solid shape with a polygon base and vertical faces perpendicular to the base. (D) Signup and view all the answers

How is the volume of a cylinder calculated?

$V = πr²h$ (A) Signup and view all the answers

What does surface area represent in relation to a geometric solid?

The total area of all surfaces of the solid. (B) Signup and view all the answers

For which shape is the area formula $A = ½ × (a + b) × h$ applicable?

Trapezium (C) Signup and view all the answers

What is the surface area calculation method for a triangular prism?

Sum of the areas of two triangles and three rectangles. (D) Signup and view all the answers

What is the area formula for a square?

$A = s²$ (D) Signup and view all the answers

What is defined as the three-dimensional space occupied by an object?

Volume (C) Signup and view all the answers

What happens to the volume of a rectangular prism when two dimensions are multiplied by a factor of $k$?

The volume is multiplied by $k^2$. (D) Signup and view all the answers

How is the surface area of a rectangular prism affected when all dimensions are multiplied by a factor of $k$?

The surface area is multiplied by $k^2$. (A) Signup and view all the answers

What is the volume of a cylinder after multiplying the radius by a factor of $k$?

The volume is multiplied by $k^2$. (B) Signup and view all the answers

Which expression represents the surface area of a cylinder when the height is multiplied by $k$?

$kA$ (A) Signup and view all the answers

What is the change in the volume of a rectangular prism when one dimension is increased by a factor of 5?

The volume increases by a factor of 5. (B) Signup and view all the answers

When all dimensions of a prism are multiplied by $k$, what will be the new volume in relation to the original volume?

$k^3V$ (C) Signup and view all the answers

What occurs to the surface area of a rectangular prism when two dimensions are multiplied by 5?

The surface area is multiplied by 10. (C) Signup and view all the answers

If the height of a cylinder is scaled by a factor of $k$, how does it affect its volume?

The volume is multiplied by $k$. (D) Signup and view all the answers

What is the formula for the volume of a right cone?

$\frac{1}{3} \pi r^2 H$ (D) Signup and view all the answers

How is the surface area of a sphere calculated?

4πr^2 (D) Signup and view all the answers

What happens to the volume of a prism when all dimensions are multiplied by a factor of k?

It is multiplied by $k^3$. (B) Signup and view all the answers

Calculate the volume of a square pyramid with a base length of 3 units and a height of 9 units.

27 cubic units (D) Signup and view all the answers

Which of the following describes a characteristic of a right pyramid?

The apex is perpendicular to the center of the base. (D) Signup and view all the answers

What is the surface area formula for a right cone?

$\pi r (r + h)$ (C) Signup and view all the answers

What describes the volume of a sphere?

$\frac{4}{3} \pi r^3$ (D) Signup and view all the answers

Which of the following statements is correct regarding right prisms?

The lateral faces are parallelograms. (B) Signup and view all the answers

What is the formula for calculating the area of a parallelogram?

A = b × h (C) Signup and view all the answers

Which geometric solid is defined as having a polygon as its base and vertical faces perpendicular to it?

Right Prism (D) Signup and view all the answers

In the context of surface area, what does a rectangular prism consist of?

Six rectangles (D) Signup and view all the answers

What is the area of a circle with a radius of 3 units?

9π (D) Signup and view all the answers

Which formula is used to calculate the volume of a cylinder?

V = πr²h (D) Signup and view all the answers

How is the surface area of a triangular prism calculated?

Two triangles and three rectangles (A) Signup and view all the answers

Which of the following statements best describes volume?

It is the three-dimensional space occupied by an object. (A) Signup and view all the answers

What is the area formula used to calculate the area of a triangle?

A = ½ × b × h (A) Signup and view all the answers

What is the volume formula for a triangular prism?

Volume = (1/2 × base × height of triangle) × height of prism (B) Signup and view all the answers

Which statement correctly characterizes a right cone?

It has a circular base and an apex perpendicular to the base. (C) Signup and view all the answers

What happens to the volume of a prism when all dimensions are multiplied by a factor of k?

The volume increases by a factor of $k^3$. (A) Signup and view all the answers

What is the formula for the surface area of a sphere?

Surface Area = 4πr^2 (D) Signup and view all the answers

How is the volume of a square pyramid calculated?

Volume = (1/3) × base^2 × height (D) Signup and view all the answers

What characterizes a sphere compared to other shapes?

It is perfectly round and equal from all angles. (D) Signup and view all the answers

Which formula is used to calculate the volume of a right cone?

Volume = (1/3)πr^2H (B) Signup and view all the answers

Which statement about right prisms is true?

They are defined by having two parallel bases connected by rectangular faces. (D) Signup and view all the answers

What happens to the volume of a rectangular prism when one dimension is multiplied by a factor of $k$?

It is multiplied by $k$ (D) Signup and view all the answers

What is the effect on the surface area of a rectangular prism when all three dimensions are multiplied by a factor of $k$?

It is multiplied by $k^2$ (C) Signup and view all the answers

How does the volume of a cylinder change when the height is multiplied by a factor of $k$?

It is multiplied by $k$ (D) Signup and view all the answers

Which expression gives the surface area of a cylindrical shape when its radius is multiplied by $k$?

It is multiplied by $k^2$ (D) Signup and view all the answers

If two dimensions of a rectangular prism are multiplied by a factor of $k$, what is the effect on the volume?

It is multiplied by $k^2$ (D) Signup and view all the answers

What occurs to the surface area of a cylinder when the radius is multiplied by 5?

It is multiplied by 25 (C) Signup and view all the answers

When transforming all dimensions of a cylindrical shape by a factor of $k$, how does the volume relate to the original volume?

It is multiplied by $k^3$ (B) Signup and view all the answers

What relationship is established for the surface area of a rectangular prism when its dimensions are uniformly scaled by a factor of $k$?

It is multiplied by $k^2$ (D) Signup and view all the answers

What is the relationship between the volume and the height of a rectangular prism if the height is multiplied by $k$ while keeping the length and breadth constant?

The volume is multiplied by $k$ (A) Signup and view all the answers

How does the surface area of a cylinder change when the height is multiplied by a factor of $k$?

It is multiplied by $k$ (C) Signup and view all the answers

What happens to the surface area of a rectangular prism when all three dimensions are increased by a factor of $k$?

Multiplies by $k^2$ (D) Signup and view all the answers

If the radius of a cylinder is multiplied by 5, what is the new volume expressed in relation to the original volume?

25V (D) Signup and view all the answers

What is the effect on the surface area of a rectangular prism when two dimensions are multiplied by 5 and one remains unchanged?

Increases by a factor of 25 (A) Signup and view all the answers

In terms of scaling by a factor of $k$, how is the volume of a rectangular prism expressed mathematically?

V_k = k^3V (B) Signup and view all the answers

What is the impact on volume when both the length and height of a rectangular prism are multiplied by $k$?

The volume is multiplied by $k^2$ (A) Signup and view all the answers

If the surface area of a cylinder is represented as $A = rac{3}{2} imes 2 ext{π}rh$ and the height is scaled by $k$, what will be its new expression?

$rac{3}{2} imes 2 ext{π}r(kh)$ (C) Signup and view all the answers

What is the formula to calculate the area of a trapezium?

$A = ½ × (a + b) × h$ (B) Signup and view all the answers

Which statement best describes the relationship between surface area and volume?

Volume increases with the cube of the dimension scaling, while surface area increases with the square. (A) Signup and view all the answers

Which formula accurately describes how to calculate the surface area of a cylinder?

Area of two circles plus the lateral area calculated as circumference times height. (D) Signup and view all the answers

Which type of prism has triangular bases?

Triangular prism (C) Signup and view all the answers

What defines the volume of a geometric solid?

The three-dimensional space occupied by the object. (C) Signup and view all the answers

Which statement about the surface area of a cube is true?

It equals six times the area of one face. (A) Signup and view all the answers

How does the volume calculation differ between a rectangular prism and a triangular prism?

Rectangular prisms use height and width; triangular prisms use base and height. (D) Signup and view all the answers

What does the term 'right prism' specifically imply?

Vertical faces are perpendicular to the base. (B) Signup and view all the answers

What is the volume formula for a triangular prism?

Volume = $rac{1}{2} imes ext{base} imes ext{height of triangle} imes ext{height of prism}$ (C) Signup and view all the answers

Which expression correctly represents the surface area of a right cone?

Surface Area = $ ext{Area of base} + ext{Area of walls}$ (B) Signup and view all the answers

What is the volume formula for a right cone?

Volume = $rac{1}{3} imes ext{Area of base} imes ext{Height}$ (D) Signup and view all the answers

How is the volume of a sphere calculated?

Volume = $rac{4}{3} ext{π}r^3$ (D) Signup and view all the answers

Which formula describes the surface area of a triangular pyramid?

Surface Area = $rac{1}{2} b (h + 3h_s)$ (D) Signup and view all the answers

What occurs to the volume of a right pyramid when all its dimensions are multiplied by a factor of k?

The volume is multiplied by $k^3$. (C) Signup and view all the answers

What is the correct formula for calculating the surface area of a sphere?

Surface Area = $4 ext{π}r^2$ (A) Signup and view all the answers

How is the volume of a square pyramid determined?

Volume = $rac{1}{3} b^2 imes H$ (A) Signup and view all the answers

What is the volume of a triangular pyramid with a base area of 10 square units and a height of 15 units?

50 cubic units (B) Signup and view all the answers

If the height of a cone is doubled while keeping the radius constant, how will the volume change?

It will double (C) Signup and view all the answers

What is the surface area of a right cone with a radius of 4 units and a height of 3 units?

$20\pi$ square units (B) Signup and view all the answers

What will be the volume of a sphere with a radius of 3 units?

$27\pi$ cubic units (C) Signup and view all the answers

A square pyramid has a base with side length of 6 units and a height of 8 units. What is its volume?

72 cubic units (D) Signup and view all the answers

How does scaling all dimensions of a prism by a factor of $k$ affect its surface area?

It is scaled by a factor of $k^2$ (A) Signup and view all the answers

What is the surface area of a sphere with a radius of 5 units?

$50\pi$ square units (B) Signup and view all the answers

If the base radius of a cylinder is tripled while keeping the height the same, how does this affect the volume?

It will increase by a factor of 9 (D) Signup and view all the answers

What is the formula for the area of a parallelogram?

A = b × h (B) Signup and view all the answers

Which statement correctly defines the surface area of a triangular prism?

Sum of the areas of the triangular bases and the lateral surface (D) Signup and view all the answers

What is the correct volume calculation for a right prism with a polygon base?

Volume = Base Area × Height (B) Signup and view all the answers

If the radius of a cylinder is doubled, how is the volume affected?

Volume becomes four times larger (C) Signup and view all the answers

What is the surface area of a cylinder consisting of two circular bases and a lateral rectangle?

SA = 2πr² + 2πrh (D) Signup and view all the answers

Which expression best describes the method for finding the area of a trapezium?

A = ½ × (base1 + base2) × height (D) Signup and view all the answers

What distinguishes a right prism from other prisms?

All angles between the base and the vertical faces are right angles (C) Signup and view all the answers

What is the volume formula for a cylinder given its radius and height?

Volume = πr²h (B) Signup and view all the answers

What is the increase factor of the volume of a rectangular prism when one dimension is multiplied by 5?

5 times the original volume (D) Signup and view all the answers

If the surface area of a rectangular prism is given by $A = 2(lh + lb + bh)$, what is the new surface area formula when both height and width are multiplied by 5?

$A_1 = 2(5lh + lb + 5bh)$ (C) Signup and view all the answers

What is the relationship between the increase in the surface area of a cylinder when the radius is multiplied by a factor of $k$?

The surface area is multiplied by $k^2$ (A) Signup and view all the answers

What happens to the volume of a cylinder if both the radius and height are multiplied by a factor of $k$?

Volume increases by $k^3$ (A) Signup and view all the answers

What is the new surface area formula for a cube when all dimensions are multiplied by a factor of $k$?

$A_k = k^2A$ (C) Signup and view all the answers

If the volume of a rectangular prism is $V = l imes b imes h$, and only the height is multiplied by 5, what is the new volume?

$5V$ (C) Signup and view all the answers

When the height of a cylinder is multiplied by $k$, how does that affect the overall surface area?

Surface area increases by $k$ (A) Signup and view all the answers

What is the volume of a cylinder if the radius is multiplied by $k$ and the new volume relationship is given as $V_k = k^2V$?

$V_k = k^2V$ (C) Signup and view all the answers

Gr 10 Math Ch 10 SUM: Measurement

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Questions and Answers

What happens to the volume of a rectangular prism when all three dimensions are multiplied by 5?

When only the height of a cylinder is multiplied by a factor of k, how does this affect the volume?

What is the effect on the surface area of a rectangular prism if one dimension is multiplied by k?

If two dimensions of a rectangular prism are multiplied by 5, how does the surface area change?

What is the formula for the volume of a right cone?

Which of the following accurately describes the change in volume when the radius of a cylinder is multiplied by k?

How does the surface area of a pyramid change when its dimensions are multiplied by a factor of $k$?

When a rectangular prism has one dimension multiplied by k, how is the surface area affected?

What is the formula used to calculate the volume of a triangular pyramid?

If all dimensions of a cylinder are multiplied by k, how does the surface area change?

Multiply the height of a cylinder by k. What effect does this have on the surface area?

Which of the following describes a right pyramid?

What is the surface area formula for a right cone?

What is the formula for the volume of a sphere?

Which of the following correctly states the relationship between the volume and surface area when dimensions are scaled by a factor of $k$?

What is the correct surface area formula for a square pyramid?

What is the formula for calculating the area of a trapezium?

Which of the following shapes has the same formula for area as a rectangle?

How is the surface area of a triangular prism calculated?

What defines a right prism?

What is a key characteristic of the volume of a cylinder?

Which formula is used to calculate the area of a circle?

What does the surface area of a cube consist of?

Which of the following shapes does NOT belong to the category of right prisms?

What is the formula used to calculate the area of a triangle?

Which statement correctly describes a right prism?

How is the volume of a cylinder calculated?

What does surface area represent in relation to a geometric solid?

For which shape is the area formula $A = ½ × (a + b) × h$ applicable?

What is the surface area calculation method for a triangular prism?

What is the area formula for a square?

What is defined as the three-dimensional space occupied by an object?

What happens to the volume of a rectangular prism when two dimensions are multiplied by a factor of $k$?

How is the surface area of a rectangular prism affected when all dimensions are multiplied by a factor of $k$?

What is the volume of a cylinder after multiplying the radius by a factor of $k$?

Which expression represents the surface area of a cylinder when the height is multiplied by $k$?

What is the change in the volume of a rectangular prism when one dimension is increased by a factor of 5?

When all dimensions of a prism are multiplied by $k$, what will be the new volume in relation to the original volume?

What occurs to the surface area of a rectangular prism when two dimensions are multiplied by 5?

If the height of a cylinder is scaled by a factor of $k$, how does it affect its volume?

What is the formula for the volume of a right cone?

How is the surface area of a sphere calculated?

What happens to the volume of a prism when all dimensions are multiplied by a factor of k?

Calculate the volume of a square pyramid with a base length of 3 units and a height of 9 units.

Which of the following describes a characteristic of a right pyramid?

What is the surface area formula for a right cone?

What describes the volume of a sphere?

Which of the following statements is correct regarding right prisms?

What is the formula for calculating the area of a parallelogram?

Which geometric solid is defined as having a polygon as its base and vertical faces perpendicular to it?

In the context of surface area, what does a rectangular prism consist of?

What is the area of a circle with a radius of 3 units?

Which formula is used to calculate the volume of a cylinder?

How is the surface area of a triangular prism calculated?

Which of the following statements best describes volume?

What is the area formula used to calculate the area of a triangle?

What is the volume formula for a triangular prism?

Which statement correctly characterizes a right cone?

What happens to the volume of a prism when all dimensions are multiplied by a factor of k?

What is the formula for the surface area of a sphere?

How is the volume of a square pyramid calculated?

What characterizes a sphere compared to other shapes?

Which formula is used to calculate the volume of a right cone?

Which statement about right prisms is true?

What happens to the volume of a rectangular prism when one dimension is multiplied by a factor of $k$?

What is the effect on the surface area of a rectangular prism when all three dimensions are multiplied by a factor of $k$?

How does the volume of a cylinder change when the height is multiplied by a factor of $k$?

Which expression gives the surface area of a cylindrical shape when its radius is multiplied by $k$?

If two dimensions of a rectangular prism are multiplied by a factor of $k$, what is the effect on the volume?

What occurs to the surface area of a cylinder when the radius is multiplied by 5?

When transforming all dimensions of a cylindrical shape by a factor of $k$, how does the volume relate to the original volume?

What relationship is established for the surface area of a rectangular prism when its dimensions are uniformly scaled by a factor of $k$?

What is the relationship between the volume and the height of a rectangular prism if the height is multiplied by $k$ while keeping the length and breadth constant?

How does the surface area of a cylinder change when the height is multiplied by a factor of $k$?

What happens to the surface area of a rectangular prism when all three dimensions are increased by a factor of $k$?

If the radius of a cylinder is multiplied by 5, what is the new volume expressed in relation to the original volume?