Problem

The sum of the legs of a right triangle is 9 cm. When the triangle rotates about one of the legs, a cone results which has the maximum volume. Then a. slant height of such a cone is

3\sqrt{5}

b. maximum volume of the cone is

32\pi

c. curved surface of the cone is

18\sqrt{5}\pi

d. semi vertical angle of cone is

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

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