Question

The volume of frustum of a cone is 180.27 ft${}^3$. The area of the bottom circle of the cone is 27 ft${}^2$ and the area of the top circle of the cone is 12 ft${}^2$. Find its height.

• A. 9.28 ft
• B. 9.38 ft
• C. 9.58 ft
• D. 9.48 ft

Answer 1

Answer: (D)

9.48 ft

Volume of the frustum cone is V = $\frac{h}{3}[A_1+A_2+\sqrt{A_1{A}_2}$]

Area of the bottom cone, A${}_1$ = 27 ft${}^2$

Area of the top cone, A${}_2$ = 12 ft${}^2$

Height = ?

Volume = 180.27 ft${}^3$

$180.27=h/3[27+12+\sqrt{37\times 12}]$

$180.27\times 3=h[39+\sqrt{324}]$

$540.81=h[39+18]$

$\frac{540.81}{57}=h$

$h=9.48ft$