Question

The volume of the frustum of a cone is 54 cm${}^3$ and its height is 6 cm, bottom radius, R = 1 cm. Find its top radius, r. (Use $\pi$ = 3).

• A. 2 cm
• B. 3 cm
• C. 4 cm
• D. 5 cm

Answer 1

The correct option is A 2 cm

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

Radius, R = 1 cm, r = ?, h = 6 cm

Volume = 54 cm${}^3$

$54=(3\times 6)/\left(3\right)[1^2+1\times r+r^2]$

$54=6[1+r+r^2]$

$9=1+r+r^2$

$r^2+r-8=0$

On factoring neglect the negative value of r, we get

r = 2 cm