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Show that the right circular cone of least curved surface area and given volume is 2 times the radius of the base.

Show that the right circular cone of least curved surface area and given volume is 2 times the radius of the base.

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
V = (1/3)π(r^2)h or h = 3V/(πr^2) or h^2 = (9V^2)/{(πr^2)^2} ---------------------- 1
Area, S, of curved surface = (1/2)*(2πr)*√(r^2 + h^2) = πr√(r^2 + h^2) or
S^2 = {(πr)^2}(r^2 + h^2) = π^2 r^4 + (9V^2)/(r^2) [Usng 1]
2S*(dS/dr) = 4π^2r^3 - {18V^2}/r^3 = 0 ----------------------------- 2 or
4π^2 * r^6 = 18V^2 =(18/9)π^2 *r^4 *h^2 or
2r^2 = h^2
h = √(2)*r
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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