Question

The volume of the frustum of a cone is 1,200 mm${}^3$. The bottom and top radius are D = 5 mm and d = 1 mm. Find its height. (Use $\pi$ = 3).

• A. 20 mm
• B. 30 mm
• C. 40 mm
• D. 9.67 mm

Answer 1

The correct option is D 9.67 mm

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

D = 5 mm, d = 1 mm, h = ?

Diameter = radius/2

Radius, R = 10 mm, r = 2mm

Volume = 1,200 mm${}^3$

$1,200=(3\times h)/\left(3\right)[{10}^2+10\times 2+2^2]$

$1,200=h[100+20+4]$

$1,200=h\left[124\right]$

$\frac{1,200}{124}=h$

$h=9.67mm$