Gr 10 Math Ch 10: The effect of multiplying a dimension by a factor of k

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

The volume is multiplied by $k^3$ (correct)

The volume remains the same

The volume is multiplied by $k^2$

The volume is multiplied by $k^4$

If the height of a cylinder is increased by a factor of k, how is the surface area affected?

The surface area is multiplied by $k$ (correct)

The surface area is multiplied by $k^3$

The surface area is multiplied by $k^2$

The surface area remains unchanged

When the radius of a cylinder is multiplied by a factor of k, how does the surface area change?

The surface area decreases by a factor of $k^2$

The surface area increases by a factor of $k$

The surface area remains the same

The surface area increases by a factor of $k^2$ (correct)

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

The volume increases by a factor of 4 Signup and view all the answers

What is the relationship between the change in radius and the change in volume for a cylinder?

The volume changes by the square of the factor of the radius change Signup and view all the answers

When both the radius and height of a cylinder are multiplied by k, how does the surface area change in comparison to the volume?

Surface area increases by a factor of $k^2$, volume increases by a factor of $k^3$ Signup and view all the answers

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

The volume is multiplied by 5. Signup and view all the answers

How is the surface area affected when two dimensions of a rectangular prism are multiplied by a factor of 5?

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

What is the formula for the volume of a rectangular prism when all dimensions are multiplied by a factor of k?

$V_k = k^3 V$ Signup and view all the answers

If the original surface area of a rectangular prism is A, what will the new surface area be when all dimensions are multiplied by k?

$k^2 A$ Signup and view all the answers

Which of the following statements correctly describes the change in volume and surface area when one dimension is multiplied by k?

Volume is multiplied by k, surface area by k^2. Signup and view all the answers

What volume change occurs when all three dimensions of a rectangular prism are multiplied by a factor of 5?

Volume increases to 125V. Signup and view all the answers

What happens to the surface area when both dimensions of a rectangular prism are multiplied by 2?

The surface area is multiplied by 4. Signup and view all the answers

Which of these correctly describes how the volume and surface area change when all dimensions are multiplied by a factor of k?

Volume changes by $k^3$, surface area by $k^2$. Signup and view all the answers

What is the effect on the volume of a cylinder when the radius is multiplied by 3?

Volume is multiplied by 9 Signup and view all the answers

How does the surface area of a cylinder change when the height is doubled?

Surface area is doubled Signup and view all the answers

If the radius of a cylinder is tripled, what is the new surface area in relation to the original surface area?

Surface area is 9 times the original Signup and view all the answers

When the radius of a cylinder is multiplied by k, how is the effect on volume described?

Volume is increased by a factor of k² Signup and view all the answers

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

Volume is multiplied by k³ Signup and view all the answers

How does the surface area change if only the height of a cylinder is multiplied by k?

Surface area increases by a factor of k Signup and view all the answers

What happens to the volume of a rectangular prism when its height is multiplied by a factor of 5?

It increases by a factor of 5. Signup and view all the answers

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

It increases by a factor of k^2. Signup and view all the answers

If the original volume of a rectangular prism is V, what is the new volume after multiplying all dimensions by 3?

27V Signup and view all the answers

When two dimensions of a rectangular prism are multiplied by a factor of k, what is the new volume in terms of the original volume V?

k^2V Signup and view all the answers

What is the relationship between the factor applied to dimensions and the resulting volume of a rectangular prism?

The volume changes by the cube of the factor applied. Signup and view all the answers

If one dimension of a rectangular prism is doubled and the second dimension remains unchanged, how does the surface area change?

It is doubled. Signup and view all the answers

What effect does multiplying all dimensions of a cylinder by a factor of k have on its volume?

Volume increases by a factor of k^3. Signup and view all the answers

Which statement correctly describes the change in volume when only the height of a prism is multiplied by a factor of k?

The volume increases by a factor of k. Signup and view all the answers

What happens to the volume of a cylinder when the height is multiplied by a factor of k?

It is multiplied by k Signup and view all the answers

When the radius of a cylinder is increased by a factor of k, how much does the surface area increase?

Increases by a factor of k^2 Signup and view all the answers

If both the radius and height of a cylinder are multiplied by k, how does the volume change?

It is multiplied by k^3 Signup and view all the answers

What is the relationship between the change in radius and the surface area of a cylinder?

Surface area increases by a factor of k^2 Signup and view all the answers

When the height of a cylinder is multiplied by k and the radius remains unchanged, how does the surface area change?

It is multiplied by k Signup and view all the answers

How does the volume change when both the height and radius of a cylinder are multiplied by k?

It is multiplied by k^3 Signup and view all the answers

What is the volume of a rectangular prism when all dimensions are multiplied by a factor of 3 if the original volume is V?

27V Signup and view all the answers

How is the new surface area determined when one dimension of a prism is multiplied by 2?

The surface area is multiplied by 4. Signup and view all the answers

What happens to the surface area of a rectangular prism if two dimensions are multiplied by 3 and one dimension remains unchanged?

The surface area is multiplied by 12. Signup and view all the answers

If the surface area of a rectangular prism is represented as A, what will it be when one dimension is multiplied by k?

k^2A Signup and view all the answers

What will be the new volume of a rectangular prism after each dimension is increased by a factor of 4?

64V Signup and view all the answers

When both height and breadth of a prism are multiplied by k while length remains unchanged, what is the relationship of the new volume V_k to the original volume V?

V_k = k^2V Signup and view all the answers

If the volume of a cylinder is expressed as V and the height is increased by a factor of 2 while the radius is unchanged, what is the new volume in relation to the original volume?

2V Signup and view all the answers

What happens to the surface area of a rectangular prism if all dimensions are multiplied by a factor of k?

It is multiplied by k^2. Signup and view all the answers

What happens to the volume of a cylinder when the height is multiplied by a factor of k?

The volume is multiplied by k Signup and view all the answers

If the radius of a cylinder is increased by a factor of k, how does the surface area change?

The surface area is multiplied by k^2 Signup and view all the answers

When both the radius and height of a cylinder are multiplied by k, how is the change in volume described?

The volume is multiplied by k^3 Signup and view all the answers

What effect does multiplying only the height of a cylinder by k have on its surface area?

The surface area is multiplied by k Signup and view all the answers

If the original surface area of a cylinder is A, what will the new surface area be when the radius is doubled and the height remains unchanged?

4A Signup and view all the answers

Gr 10 Math Ch 10: The effect of multiplying a dimension by a factor of k

Questions and Answers

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

If the height of a cylinder is increased by a factor of k, how is the surface area affected?

When the radius of a cylinder is multiplied by a factor of k, how does the surface area change?

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

What is the relationship between the change in radius and the change in volume for a cylinder?

When both the radius and height of a cylinder are multiplied by k, how does the surface area change in comparison to the volume?

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

How is the surface area affected when two dimensions of a rectangular prism are multiplied by a factor of 5?

What is the formula for the volume of a rectangular prism when all dimensions are multiplied by a factor of k?

If the original surface area of a rectangular prism is A, what will the new surface area be when all dimensions are multiplied by k?

Which of the following statements correctly describes the change in volume and surface area when one dimension is multiplied by k?

What volume change occurs when all three dimensions of a rectangular prism are multiplied by a factor of 5?

What happens to the surface area when both dimensions of a rectangular prism are multiplied by 2?

Which of these correctly describes how the volume and surface area change when all dimensions are multiplied by a factor of k?

What is the effect on the volume of a cylinder when the radius is multiplied by 3?

How does the surface area of a cylinder change when the height is doubled?

If the radius of a cylinder is tripled, what is the new surface area in relation to the original surface area?

When the radius of a cylinder is multiplied by k, how is the effect on volume described?

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

How does the surface area change if only the height of a cylinder is multiplied by k?

What happens to the volume of a rectangular prism when its height is multiplied by a factor of 5?

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

If the original volume of a rectangular prism is V, what is the new volume after multiplying all dimensions by 3?

When two dimensions of a rectangular prism are multiplied by a factor of k, what is the new volume in terms of the original volume V?

What is the relationship between the factor applied to dimensions and the resulting volume of a rectangular prism?

If one dimension of a rectangular prism is doubled and the second dimension remains unchanged, how does the surface area change?

What effect does multiplying all dimensions of a cylinder by a factor of k have on its volume?

Which statement correctly describes the change in volume when only the height of a prism is multiplied by a factor of k?

What happens to the volume of a cylinder when the height is multiplied by a factor of k?

When the radius of a cylinder is increased by a factor of k, how much does the surface area increase?

If both the radius and height of a cylinder are multiplied by k, how does the volume change?

What is the relationship between the change in radius and the surface area of a cylinder?

When the height of a cylinder is multiplied by k and the radius remains unchanged, how does the surface area change?

How does the volume change when both the height and radius of a cylinder are multiplied by k?

What is the volume of a rectangular prism when all dimensions are multiplied by a factor of 3 if the original volume is V?

How is the new surface area determined when one dimension of a prism is multiplied by 2?

What happens to the surface area of a rectangular prism if two dimensions are multiplied by 3 and one dimension remains unchanged?

If the surface area of a rectangular prism is represented as A, what will it be when one dimension is multiplied by k?

What will be the new volume of a rectangular prism after each dimension is increased by a factor of 4?

When both height and breadth of a prism are multiplied by k while length remains unchanged, what is the relationship of the new volume V_k to the original volume V?

If the volume of a cylinder is expressed as V and the height is increased by a factor of 2 while the radius is unchanged, what is the new volume in relation to the original volume?

What happens to the surface area of a rectangular prism if all dimensions are multiplied by a factor of k?

What happens to the volume of a cylinder when the height is multiplied by a factor of k?

If the radius of a cylinder is increased by a factor of k, how does the surface area change?

When both the radius and height of a cylinder are multiplied by k, how is the change in volume described?

What effect does multiplying only the height of a cylinder by k have on its surface area?

If the original surface area of a cylinder is A, what will the new surface area be when the radius is doubled and the height remains unchanged?

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