Question

The volume of the frustum of a cone is 4,200 mm${}^3$. The bottom and top radius are R = 20 mm and r = 10 mm. Find its height. (Use $\pi$ = 3). Round off your answer to nearest whole number.

• A. 6 mm
• B. 7 mm
• C. 8 mm
• D. 10 mm

Answer 1

The correct option is A 6 mm

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

R = 20 mm, r = 10 mm, h = ?

Volume = 4,200 mm${}^3$

$4,200=(3\times h)/\left(3\right)[{20}^2+20\times 10+{10}^2]$

$4,200=h[400+200+100]$

$4,200=h\left[700\right]$

$\frac{4,200}{700}=h$

h = 6 mm