Question

The height of the frustum cone is 270 ft. The area of the top and bottom circle of the cone is 8 ft${}^2$ and 32 ft${}^2$ respectively. Find its volume.

• A. 14,440 ft${}^3$
• B. 13,440 ft${}^3$
• C. 12,440 ft${}^3$
• D. 10,440 ft${}^3$

Answer 1

The correct option is D 10,440 ft${}^3$

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 = 8 ft${}^2$

Area of the bottom cone = 32 ft${}^2$

Height = 270 ft

Volume = $\frac{270}{3}[8+32+\sqrt{8\times 32}$]

$=90[40+\sqrt{256}]$

$=90[100+16]$

$=90\times 116$

$=10,440f{t}^3$