What happens to the volume of a cylinder when the dimension is multiplied by 4?

Question

Does the volume also multiply by 4?

Answer 1

Which dimension? Volume of a cylinder is pi r squared x height. If the height is 4x then volume is too. If radius is 4x then volume is 16x

Answer 2

Let's take a look and see!

When you say the dimension of a cylinder I believe you mean the height and the radius

We know the volume of a cylinder is Volume= V = H × π × R²

Where H = height and R = radius and π = (22/7) (π is the ratio of the circumference of a circle to the radius!)

If we multiple the dimensions by 4 then our new value for height H' = 4H and our new value for radius R'= 4R so our new volume V' is now :

V' = H' × π × R'² substituting our values for H and R for H' and R' gives

V' = 4H × π ×( 4R)² = 4H × π ×16R² = 64 × H × π × R² So V' = 64 × H × π × R² = 64V

This is 64 times the original volume since V = H × π × R²

So if we multiply the dimensions of a cylinder (i.e the radius and the height) by 4 our Volume is multiplied by 64!

If we multiply only the radius by 4 then our Volume is only multiplied by 16 since our radius is squared.

If we multiply only the height by 4 then our Volume is only multiplied by 4 .