Question

The radius of the base of a right circular cylinder is halved and the height is doubled. What is the ratio of the volume of the new cylinder to that of the original one.

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Answer 1

Step-by-step explanation:

Given:-

The radius of the base of a right circular cylinder is halved and the height is doubled.

To find:-

What is the ratio of the volume of the new cylinder to that of the original one.

Solution:-

Let the radius of the base of a right circular cylinder be 'r' units

and it's height be 'h' units

Volume of a cylinder = πr^2h cubic units

V1 = πr^2h cubic units -----------(1)

Now if the radius is halved then the radius of the new cylinder = r/2 units

If the height is doubled then the height of the new cylinder =2h units

Volume of the new cylinder =

V2 = π(r/2)^2×(2h) cubic units

=>V2 = π×(r^2/4)×2h

=>V2 = π×r^2×2h/4

=>V2 = πr^2h/2 cubic units----------(2)

Ratio of the volume of new cylinder to the original cylinder = V2:V1

=>πr^2h/2 : πr^2h

=>(πr^2h/2)/(πr^2h)

=>(1/2):1

=>1:2

Ratio = 1:2

Answer:-

Ratio of the volume of new cylinder to the original cylinder = 1:2

Used formulae:-

• Volume of a cylinder = πr^2h cubic units

Answer 2

Refer to the attachment please.