The rate of change of volume of sphere with respect to its surface area S is
A
√Sπ
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B
12√Sπ
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C
14√Sπ
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D
4√Sπ
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Solution
The correct option is C14√Sπ Volume of sphere with radius r is 43πr3 and surface area S=πr2 ∴dVdr=43π(3r2)=4πr2 Now S=4πr2 dSdr=4π(2r) ∴dVdS=dVdSdSdr=4πr28πr=r2 =12(r)...(1) Now S=4πr2 ∴r2=S4π r=12(√Sπ) ∴ Rate of change of volume w,r,to S=12[12(√Sπ)]=14(√Sπ)