Question

A baloon, which always remains spherical has a veriable radius. find the rate at which its volume is increasing with the radius when the later is 10 cm.

Answer 1

here's the answer.......

solution
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Toolbox:If y=f(x)y=f(x),then dydxdydx measures the rate of change of yy w.r.t xx.(dydx)x=x0(dydx)x=x0 represents the rate of change of yy w.r.t xx at x=x0x=x0

Step 1:

Volume of the sphere is v=43v=43πr3πr3

Radius r=10cmr=10cm

Hence differentiating w.r.t rr on both sides,

dvdr=43dvdr=43π3r2π3r2

Step 2:

Substituting the values for rr we get,

dvdrdvdr=43=43π×3(10)2π×3(10)2

=400πcm3/cm=400πcm3/cm

Hence the rate at which the volume is increasing is 400πcm3/cm