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