Question

The volume of frustum of a cone is 270.15 mm${}^3$. The area of the bottom circle of the cone is 20 mm${}^2$ and the area of the top circle of the cone is 5 mm${}^2$. Find its height.

• A. 13.15 mm
• B. 22.15 mm
• C. 23.15 mm
• D. 24.15 mm

Answer 1

Answer: (C)

23.15 mm

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${}_1$ = 20 mm${}^2$

Area of the top cone, A${}_2$ = 5 mm${}^2$

Height = ?

Volume = 270.15 mm${}^3$

$270.15=h/3[20+5+\sqrt{20\times 5}]$

$270.15\times 3=h[25+\sqrt{10}]$

$810.45=h[25+10]$

$\frac{810.45}{35}=h$

$h=23.15mm$