For a right circular cone

MATHEMATICS · Multi-part · CBSE · Mathematics · Surface Areas and Volumes · Surface Areas and Volumes

Problem

For a right circular cone, the numerical value of its curved surface area (in cm2\text{cm}^{2}) is equal to the numerical value of its volume (in cm3\text{cm}^{3}). The slant height of the cone is 10 cm10\,\text{cm}. (i) Show that the radius rr of the base satisfies the quadratic equation r4−100r2+900=0r^{4}-100r^{2}+900=0 and hence find the two possible values of rr. (ii) For each value of rr obtained in part (i), calculate the corresponding vertical height of the cone. (iii) For each possible cone, determine its total surface area, leaving π\pi in your answer.

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