Question

The height of the frustum cone is 30 cm. The area of the top and bottom circle of the cone is 6 cm${}^2$ and 96 cm${}^2$ respectively. Find its volume.

• A. 1,260 cm${}^3$
• B. 1,700 m${}^3$
• C. 1,260 m${}^3$
• D. 1,260 cm

Answer 1

The correct option is A 1,260 cm${}^3$

Volume of the frustum cone is V = $\frac{h}{3}[\pi R^2+\pi r^2+\sqrt{\left(\pi R^2\right)\left(\pi r^2\right)}$]

Area of the top cone = 6 cm${}^2$

Area of the bottom cone = 96 cm${}^2$

Height = 30 cm

Volume = $\frac{30}{3}[96+6+\sqrt{96x6}]$
$=10[102+\sqrt{576}]$

$=10[102+24]$

$=10\times 126$

$=$ 1,260 cm${}^3$