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?

  • 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?

    <p>The surface area is multiplied by 25.</p> Signup and view all the answers

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

    <p>$ rac{1}{3} imes ext{Area of base} imes ext{Height of cone}$</p> 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?

    <p>The volume is multiplied by $k^2$.</p> Signup and view all the answers

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

    <p>It increases by a factor of $k^2$</p> Signup and view all the answers

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

    <p>The surface area is multiplied by a factor that includes k.</p> Signup and view all the answers

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

    <p>$ rac{1}{3} imes rac{1}{2} b h imes H$</p> Signup and view all the answers

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

    <p>The surface area is multiplied by $k^2$.</p> Signup and view all the answers

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

    <p>The surface area is multiplied by k.</p> Signup and view all the answers

    Which of the following describes a right pyramid?

    <p>A solid with polygonal base and an apex directly above the center of the base</p> Signup and view all the answers

    What is the surface area formula for a right cone?

    <p>$ ext{Area of base} + ext{Area of walls}$</p> Signup and view all the answers

    What is the formula for the volume of a sphere?

    <p>$ rac{4}{3} ext{Volume} = au r^3$</p> 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 $k$?

    <p>Surface area changes by $k^2$ and volume by $k^3$</p> Signup and view all the answers

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

    <p>$b^2 + 4 imes rac{1}{2} b h_s$</p> Signup and view all the answers

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

    <p>A = ½ × (a + b) × h</p> Signup and view all the answers

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

    <p>Parallelogram</p> Signup and view all the answers

    How is the surface area of a triangular prism calculated?

    <p>Area of two triangles and three rectangles</p> Signup and view all the answers

    What defines a right prism?

    <p>The vertical faces are perpendicular to the base</p> Signup and view all the answers

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

    <p>It is calculated using πr² times the height</p> Signup and view all the answers

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

    <p>A = πr²</p> Signup and view all the answers

    What does the surface area of a cube consist of?

    <p>Six identical squares</p> Signup and view all the answers

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

    <p>Pyramid</p> Signup and view all the answers

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

    <p>$A = ½ × b × h$</p> Signup and view all the answers

    Which statement correctly describes a right prism?

    <p>A solid shape with a polygon base and vertical faces perpendicular to the base.</p> Signup and view all the answers

    How is the volume of a cylinder calculated?

    <p>$V = πr²h$</p> Signup and view all the answers

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

    <p>The total area of all surfaces of the solid.</p> Signup and view all the answers

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

    <p>Trapezium</p> Signup and view all the answers

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

    <p>Sum of the areas of two triangles and three rectangles.</p> Signup and view all the answers

    What is the area formula for a square?

    <p>$A = s²$</p> Signup and view all the answers

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

    <p>Volume</p> Signup and view all the answers

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

    <p>The volume is multiplied by $k^2$.</p> 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 $k$?

    <p>The surface area is multiplied by $k^2$.</p> Signup and view all the answers

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

    <p>The volume is multiplied by $k^2$.</p> Signup and view all the answers

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

    <p>$kA$</p> 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?

    <p>The volume increases by a factor of 5.</p> 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?

    <p>$k^3V$</p> Signup and view all the answers

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

    <p>The surface area is multiplied by 10.</p> 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?

    <p>The volume is multiplied by $k$.</p> Signup and view all the answers

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

    <p>$\frac{1}{3} \pi r^2 H$</p> Signup and view all the answers

    How is the surface area of a sphere calculated?

    <p>4πr^2</p> Signup and view all the answers

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

    <p>It is multiplied by $k^3$.</p> 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.

    <p>27 cubic units</p> Signup and view all the answers

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

    <p>The apex is perpendicular to the center of the base.</p> Signup and view all the answers

    What is the surface area formula for a right cone?

    <p>$\pi r (r + h)$</p> Signup and view all the answers

    What describes the volume of a sphere?

    <p>$\frac{4}{3} \pi r^3$</p> Signup and view all the answers

    Which of the following statements is correct regarding right prisms?

    <p>The lateral faces are parallelograms.</p> Signup and view all the answers

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

    <p>A = b × h</p> Signup and view all the answers

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

    <p>Right Prism</p> Signup and view all the answers

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

    <p>Six rectangles</p> Signup and view all the answers

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

    <p>9π</p> Signup and view all the answers

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

    <p>V = πr²h</p> Signup and view all the answers

    How is the surface area of a triangular prism calculated?

    <p>Two triangles and three rectangles</p> Signup and view all the answers

    Which of the following statements best describes volume?

    <p>It is the three-dimensional space occupied by an object.</p> Signup and view all the answers

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

    <p>A = ½ × b × h</p> Signup and view all the answers

    What is the volume formula for a triangular prism?

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

    Which statement correctly characterizes a right cone?

    <p>It has a circular base and an apex perpendicular to the base.</p> Signup and view all the answers

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

    <p>The volume increases by a factor of $k^3$.</p> Signup and view all the answers

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

    <p>Surface Area = 4πr^2</p> Signup and view all the answers

    How is the volume of a square pyramid calculated?

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

    What characterizes a sphere compared to other shapes?

    <p>It is perfectly round and equal from all angles.</p> Signup and view all the answers

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

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

    Which statement about right prisms is true?

    <p>They are defined by having two parallel bases connected by rectangular faces.</p> Signup and view all the answers

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

    <p>It is multiplied by $k$</p> 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 $k$?

    <p>It is multiplied by $k^2$</p> Signup and view all the answers

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

    <p>It is multiplied by $k$</p> Signup and view all the answers

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

    <p>It is multiplied by $k^2$</p> 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?

    <p>It is multiplied by $k^2$</p> Signup and view all the answers

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

    <p>It is multiplied by 25</p> 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?

    <p>It is multiplied by $k^3$</p> 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 $k$?

    <p>It is multiplied by $k^2$</p> 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?

    <p>The volume is multiplied by $k$</p> Signup and view all the answers

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

    <p>It is multiplied by $k$</p> 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 $k$?

    <p>Multiplies by $k^2$</p> 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?

    <p>25V</p> 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?

    <p>Increases by a factor of 25</p> 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?

    <p>V_k = k^3V</p> 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 $k$?

    <p>The volume is multiplied by $k^2$</p> 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?

    <p>$ rac{3}{2} imes 2 ext{π}r(kh)$</p> Signup and view all the answers

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

    <p>$A = ½ × (a + b) × h$</p> Signup and view all the answers

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

    <p>Volume increases with the cube of the dimension scaling, while surface area increases with the square.</p> Signup and view all the answers

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

    <p>Area of two circles plus the lateral area calculated as circumference times height.</p> Signup and view all the answers

    Which type of prism has triangular bases?

    <p>Triangular prism</p> Signup and view all the answers

    What defines the volume of a geometric solid?

    <p>The three-dimensional space occupied by the object.</p> Signup and view all the answers

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

    <p>It equals six times the area of one face.</p> Signup and view all the answers

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

    <p>Rectangular prisms use height and width; triangular prisms use base and height.</p> Signup and view all the answers

    What does the term 'right prism' specifically imply?

    <p>Vertical faces are perpendicular to the base.</p> Signup and view all the answers

    What is the volume formula for a triangular prism?

    <p>Volume = $ rac{1}{2} imes ext{base} imes ext{height of triangle} imes ext{height of prism}$</p> Signup and view all the answers

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

    <p>Surface Area = $ ext{Area of base} + ext{Area of walls}$</p> Signup and view all the answers

    What is the volume formula for a right cone?

    <p>Volume = $ rac{1}{3} imes ext{Area of base} imes ext{Height}$</p> Signup and view all the answers

    How is the volume of a sphere calculated?

    <p>Volume = $ rac{4}{3} ext{π}r^3$</p> Signup and view all the answers

    Which formula describes the surface area of a triangular pyramid?

    <p>Surface Area = $ rac{1}{2} b (h + 3h_s)$</p> 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?

    <p>The volume is multiplied by $k^3$.</p> Signup and view all the answers

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

    <p>Surface Area = $4 ext{π}r^2$</p> Signup and view all the answers

    How is the volume of a square pyramid determined?

    <p>Volume = $ rac{1}{3} b^2 imes H$</p> 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?

    <p>50 cubic units</p> Signup and view all the answers

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

    <p>It will double</p> 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?

    <p>$20\pi$ square units</p> Signup and view all the answers

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

    <p>$27\pi$ cubic units</p> 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?

    <p>72 cubic units</p> Signup and view all the answers

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

    <p>It is scaled by a factor of $k^2$</p> Signup and view all the answers

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

    <p>$50\pi$ square units</p> 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?

    <p>It will increase by a factor of 9</p> Signup and view all the answers

    What is the formula for the area of a parallelogram?

    <p>A = b × h</p> Signup and view all the answers

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

    <p>Sum of the areas of the triangular bases and the lateral surface</p> Signup and view all the answers

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

    <p>Volume = Base Area × Height</p> Signup and view all the answers

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

    <p>Volume becomes four times larger</p> Signup and view all the answers

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

    <p>SA = 2πr² + 2πrh</p> Signup and view all the answers

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

    <p>A = ½ × (base1 + base2) × height</p> Signup and view all the answers

    What distinguishes a right prism from other prisms?

    <p>All angles between the base and the vertical faces are right angles</p> Signup and view all the answers

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

    <p>Volume = πr²h</p> 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?

    <p>5 times the original volume</p> 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?

    <p>$A_1 = 2(5lh + lb + 5bh)$</p> 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 $k$?

    <p>The surface area is multiplied by $k^2$</p> 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 $k$?

    <p>Volume increases by $k^3$</p> 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 $k$?

    <p>$A_k = k^2A$</p> 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?

    <p>$5V$</p> Signup and view all the answers

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

    <p>Surface area increases by $k$</p> 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 $V_k = k^2V$?

    <p>$V_k = k^2V$</p> Signup and view all the answers

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