Question

The height of the frustum cone is 1,500 ft. The area of the top and bottom circle of the cone is 20 ft${}^2$ and 80 ft${}^2$ respectively. Find its volume.

• A. $48,000$ ft${}^3$
• B. $52,000$ ft${}^3$
  
• C. $56,000$ ft${}^3$
• D. $40,000$ ft${}^3$

Answer 1

The correct option is C $56,000$ ft${}^3$

Volume of the frustum cone is V = $\frac{h}{3}[\pi R^2+\pi r^2+\pi Rr$]

Area of the top cone = 20 ft${}^2$

Area of the bottom cone = 80 ft${}^2$

Height = 1,200 ft

Volume = $\frac{1200}{3}[20+80+\sqrt{20\ast 80}$

$=400[100+\sqrt{1600}]$

$=400[100+40]$

$=400\times 140$

$=56,000$ ft${}^3$