A balloon that always remains spherical has a variable radius. The rate at which its volume is increasing is mπ cm2 with the radius when the latter is 10 cm. Find m.

Volume of the sphere = (4 / 3) πr3

The rate of change of volume with respect to the radius = dV / dr

= d [(4 / 3) πr3] / dr

= (4 / 3) π (3r2)

= 4πr2

When r = 10cm, dV / dr = 4π (10)2

= 400πcm2

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