Question

A vessel is in the form of a frustum of a cone. Its radius at top end is $10inch$ and the height is $12inch$. Its volume is $1200\pi {inch}^3$. Find its bottom radius.

• A. $8.4inch$
• B. $7.5inch$
• C. $7.6inch$
• D. $4.6inch$

Answer 1

Answer: (A)

$8.4inch$

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

$1,200\pi =\frac{\pi \times 12}{3}({10}^2+10\times r+r^2)$

$100\times 3=(144+10r+r^2)$

$300-144=10r+r^2$

$r^2+10r-156=0$

On factoring, we get

$(r-8.4)(r+18.45)=0$

$r=8.4,-18.45$

Since $r$ cannot be negative, thus the bottom radius is $8.4$ inches.