Question

The area of the base of a cone is $16\pi c{m}^2$ and its slant height is 5 cm. The volume of the cone is equal to

• A. $18\pi c{m}^3$
• B. $27\pi c{m}^3$
• C. $16\pi c{m}^3$
• D. $20\pi c{m}^3$

Answer 1

The correct option is C $16\pi c{m}^3$

Let r and h be the radius and the height of the cone, respectively.
Area of the base of cone $=16\pi c{m}^2$
$\Rightarrow \pi r^2=16\pi$
$\Rightarrow r^2=16$
⇒ r = 4 cm …..(i)
And, slant height, $l=\sqrt{r^2+h^2}$
$\Rightarrow 5=\sqrt{4^2+h^2}$
$\Rightarrow h^2=5^2-4^2=25-16=9$
$\Rightarrow h=3cm$ .....(ii)
$\therefore \text{Volume of cone}=\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\pi \times 4^2\times 3$ [From (i) and (ii)]
$=16\pi c{m}^3$
Hence, the correct answer is option (c).