The height of a right circular cone increases by $k\%$, its semi vertical angle remaining constant. Assuming $k$ to be small what is the approximate percentage increase in (i) total surface area (ii) volume?
2026-03-29 15:20:20.1774797620
Word problem based on differentiation - a right circular cone.
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We have $d(h)/dx=k/100$ now total surface area of cone is $πr(r+l)$ we get $πr.{\sqrt( r^2+k^2/10000)}$ now volume is $1/3πr^2h$ so we get$V=1/3πr^{2}k/100=1/300πr^2k$.