Question

The height of the frustum cone is 210 m. The area of the top and bottom circle of the cone is 10 m${}^2$ and 250 m${}^2$ respectively. Find its volume.

• A. 20,700 m${}^3$
• B. 21,700 m${}^3$
• C. 22,700 m${}^3$
• D. 23,700 m${}^3$

Answer 1

Answer: (B)

21,700 m${}^3$

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 = 10 m${}^2$

Area of the bottom cone = 250 m${}^2$

Height = 210 m

Volume = $\frac{210}{3}$

= 70[260 + $\sqrt{2500}$]

= 70[260 + 50]

= 70 x 310

= 21,700 m${}^3$