Question

A cone of height 24 cm has a plane base of surface area 154 cm². Find its volume.

Answer 1

Given:
Height of the cone = 24 cm
Area of the base of cone = 154 cm²
$\Rightarrow$$\mathrm{\pi }$r² = 154
$\Rightarrow$$\frac{22}{7}$r² = 154
$\Rightarrow$r² = $\frac{154\times 7}{22}$
$\Rightarrow$r² = 49
$\Rightarrow$r = $\sqrt{49}$ = 7 cm
Now,
Volume of the cone = $\frac{1}{3}\mathrm{\pi }{r}^{2}h$
= $\frac{1}{3}\times \frac{22}{7}\times 7^2\times 24$
= 1232 cm³