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A balloon, which always remains spherical, has a variable diameter (2x +1). Find the rate of changeof its volume with respect to |
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Answer» Step 1:Diameter of the sphere =32(2x+1)Therefore radius r=34(2x+1)Volume of the sphere v=43πr3Substituting for r we get,v=43π[34(2x+1)]3Step 2:Differentiating w.r.t x on both sides,dvdx=43x×(34)3×3(2x+1)2(2)=278π(2x+1)2 |
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