The sum of the legs of a right triangle is

MATHEMATICS · Multi correct · A Level · Mathematics · Differentiation · Differentiation

Problem

9\text{ cm}

. When the triangle rotates about one of the legs, a cone results which has maximum volume. Then (1) Slant height of such a cone is

3\sqrt{5}

(2) Maximum volume of the cone is

32\pi

(3) Curved surface area of the cone is

18\sqrt{5}\pi

(4) Semi-vertical angle of the cone is

\tan^{-1}\sqrt{2}