Question

X and Y are two cylinders of the same height. The base of X has diameter that is half of the diameter of the base of Y. If the height of X is doubled. The volume of X becomes

• A. equal to the volume of Y
• B. double the volume of Y
• C. half of the volume of Y
• D. greater than the volume of Y

Answer 1

The correct option is C half of the volume of Y

For cylinder $X$ For cylinder $Y$ $h_1=height$ $h_2=height$

$d_1=diameterofX$ $d_2=diameterofY$

$d_1=\frac{d_2}{2}$

$r_1=\frac{r^2}{2}$

Now $h_1=2h_2$

Volume of cylinder $=Basearea\times height$

$=\pi r^2\times h$

$=\pi r^{2}h$

$\frac{V_x}{V_y}=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}=\frac{r_2^2.2h_2}{4.r_2^2.h_2}=\frac{1}{2}$

$\Rightarrow$ Volume of cyhlinder $C$ is half the volume of $Y$.