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  • A right circular cone having maximum volume is inscribed in a sphere

Sir pls explain the solution in detail If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is :

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Posted by

Yash Sahu

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@Yash sahu

sphere and cone

r^2=R^2-(h-R)^2\\ V=\frac{1}{3}\pi r^2h\\r^2=9-(h-3)^2=6h-h^2\\V=\frac{1}{3}\pi(6h^2-h^3)\\to\ find\ extreme\ value\\\frac{dV}{dh}=0\\\Rightarrow h=4\\\therefore r^2=\sqrt{8}\\curved\ surface\ area\ of\ right\ circular\ cone\\=\pi rl=\pi r\sqrt{r^2+h^2}\\=\sqrt{8}\sqrt{8+16}\pi=\sqrt{8}\sqrt{24}\pi=\\\sqrt{8}\sqrt{8}\sqrt{3}\pi=8\sqrt(3)\pi

\\\frac{dv}{dh}=\frac{1}{3}\pi(12h-3h^2)=0\\12h-3h^2=0\\3h(4-h)=0\\h=0\:\:and\:\:h=4\\b^2=h^2-6h=1

Posted by

Safeer PP

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