Question

The height of the frustum cone is 12 ft. The area of the top and bottom circle of the cone is 4 ft${}^2$ and 4 ft${}^2$ respectively. Find its volume.

• A. 125 ft${}^3$
• B. 126 ft${}^3$
• C. 127 ft${}^3$
• D. 128 ft${}^3$

Answer 1

The correct option is D 128 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 = 4 ft${}^2$

Area of the bottom cone = 4 ft${}^2$

Height = 12 ft

Volume = $\frac{12}{3}[4+4+\sqrt{4\ast 4}$]

= 4[8 + $\sqrt{16}$]

= 4[8 + 4]

= 4 [8 + 4]

= 4 x 32

= 128 ft${}^3$