Question

A cylinder’s radius is reduced to 2/5 its original size and the height is quadrupled. How has the volume of the cylinder changed?

A.
The volume is now 8/25 the original volume.

B.
The volume is now 16/25 the original volume.

C.
The volume is now 64/25 the original volume.

D.
The volume is now 16/5 the original volume.

Answer 1

(B). The new volume of the cylinder is
`(16)/(25)` of the original volume.

Step-by-step explanation:

Let 5 r be the radius and h be the height of the cylinder.

The volume of the cylinder is

`V=\pi* r^2* h`

`V = \pi* (5r)^2* h`

`V= \pi* 25r^2* h`

A cylinder’s radius is reduced to 2/5 its original size and the height is quadrupled.

The new radius of the cylinder is

`r= (2)/(5)* 5r`

`r = 2r`

`h = 4h`

The new volume of the cylinder is

`V'=\pi*4r^2*4 h`

The ratio of the original volume and the new volume

`(V)/(V')=(\pi*25r^2* h)/(\pi* 4r^2* 4h)`

`(V)/(V')=(25)/(16)`

`V'=(16)/(25)V`

Hence, The new volume of the cylinder is
`(16)/(25)` of the original volume.

Answer 2

"The volume is now 16/25 the original volume" is the way among the choices given in the question that the volume of the cylinder changed. The correct option among all the options that are given in the question is the second option or option "B". I hope the answer has actually come to your great help.