Question

The circumference of the base of a cone is 44 cm and its slant height is 25 cm. Find the volume of the cone.

• A. $1232c{m}^3$
• B. $1232000c{m}^3$
• C. $681c{m}^3$
• D. $6.81c{m}^3$

Answer 1

The correct option is A $1232c{m}^3$

Given,

l = 25 cm

$2\pi r=44$

Hence,

$\Rightarrow r=\frac{44\times 7}{2\times 22}=7cm$

we know ($l^2$ = $r^2$ + $h^2$)

$\Rightarrow$ $h=\sqrt{l^2-r^2}$

$\Rightarrow$ $h=\sqrt{{25}^2-7^2}$

$\Rightarrow$ $h=\sqrt{625-49}$

$\Rightarrow h=24cm$

Volume =$\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 24$

$=1232c{m}^3$