Q. 19

The radius

Answer :

Let r be the radius of sphere and V be the volume

Let r1 = 10 cm and r2 = 9.8 cm

The change dr is given by dr = r2 – r1

dr = 9.8 – 10 = -0.2 cm …(i)

Now volume of sphere is given by

As we have to find the change in V (that is dV) with respect to r, we have to differentiate V with respect to r

dV = 4πr2dr

The radius is shrinked from 10 cm hence r will be 10 and put dr value from (i)

dV = 4π(10)2(-0.2)

dV = -4π(20)

dV = -80π

The negative sign indicates that the volume is decreased

Hence the change in volume or decrease in volume is 80π cm3

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