Question

A right triangle whose hypotenuse is $\sqrt{3} m$ long is revolved about one of its legs to generate a right circular cone. The volume of the greatest cone in cu.m. made this way is

• A. $\frac{2 \pi}{3}$
• B. $\frac{\pi}{3}$
• C. $2 \pi$
• D. none

Answer 1

Answer: (A)

$ V=\frac{1}{3} \pi x^2 y$ and $x^2+y^2=3$
$V =\frac{1}{3} \pi y \left(3- y ^2\right)$
$V ^{\prime}( y )=\frac{\pi}{3}\left(3-3 y ^2\right)=0 \Rightarrow y =1$