The sum of the legs of a right triangle is \( 9 \mathrm{~cm} \). When the triangle rotates about...

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The sum of the legs of a right triangle is \( 9 \mathrm{~cm} \). When the triangle rotates about one of the 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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