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How to derive the formula for surface area of a sphere

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$Let;radius;of;sphere;be;R;and; heta;be;the;vertical;angle\* consider;the;figure,\*Now,;select;the;thin;strip;at;an;angle;of;d heta\* Rightarrow thickness;will;be=Rd heta\* Now,;we;can;think;it;as;a;cylinder;with ; radius=R sin heta,;height=rd heta\* Rightarrow surface;area,A=2pi r h\* Rightarrow dA=2pi Rsin heta Rd heta\* Integrate;both;side;\* A ightarrow 0;to;A;and; heta ightarrow 0;to;pi\*Rightarrow int_0^A dA=int_0^pi 2pi R^2 sin heta d heta\* Rightarrow A=2pi R^2[-cos pi - (-cos 0)]\*ecause cos pi =-1;and;cos 0=1 \*A=2pi R^2(2)\*Rightarrow A=4pi R^2\* So,;Surface;area;of;Sphere;is;4pi R^2$

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Deependra Verma

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