Question

The volume of the cylinder is $96\pi m^3$. Find the volume of a cone and height if cone has same base and height as of cylinder. The circular base of the cylinder is $3$ m radius.

• A. $32{cm}^3,10.6$ m
• B. $32{cm}^3,9.6$ m
• C. $32{cm}^3,8.6$ m
• D. $32{cm}^3,7.6$ m

Answer 1

The correct option is A $32{cm}^3,10.6$ m

Volume of a cone $=$ $\frac{1}{3}\times$ Volume of a cylinder
$=\frac{1}{3}\times 96\pi$
$=32\pi m^3$
Volume of a cone $=\frac{1}{3}\times \pi r^{2}h$
$\therefore 32\pi =\frac{1}{3}\times \pi \times 3\times 3\times h$
$\therefore \frac{32\times 3}{3\times 3}=h$
$\therefore h=10.6$ m