Answer:
(B). The new volume of the cylinder is [tex]\dfrac{16}{25}[/tex] of the original volume.
Explanation:
Let 5 r be the radius and h be the height of the cylinder.
The volume of the cylinder is
[tex]V=\pi\times r^2\times h[/tex]
[tex]V = \pi\times (5r)^2\times h[/tex]
[tex]V= \pi\times 25r^2\times h[/tex]
A cylinder’s radius is reduced to 2/5 its original size and the height is quadrupled.
The new radius of the cylinder is
[tex]r= \dfrac{2}{5}\times 5r[/tex]
[tex]r = 2r[/tex]
[tex]h = 4h[/tex]
The new volume of the cylinder is
[tex]V'=\pi\times4r^2\times4 h[/tex]
The ratio of the original volume and the new volume
[tex]\dfrac{V}{V'}=\dfrac{\pi\times25r^2\times h}{\pi\times 4r^2\times 4h}[/tex]
[tex]\dfrac{V}{V'}=\dfrac{25}{16}[/tex]
[tex]V'=\dfrac{16}{25}V[/tex]
Hence, The new volume of the cylinder is [tex]\dfrac{16}{25}[/tex] of the original volume.
