Question

Ratio of a ballon changes from 7cm to 9cm .Calculate change in its volume with respect to radius.

Integration nd differentiation.​

Answer 1

$\underline{\Huge\mathfrak{Answer-}}$

We know that ;-

$= > v = \frac{4}{3} \pi \: r ^{3}$

$= > \frac{dv}{dr} = \frac{4}{3} \times \pi3 \: r^{2}$

$= > \frac{dv}{dr} = 4\pi \: r^{2}$

Now ,

The change in Volume ;-

=> V = 4πr² ( Here r = 7 )

$= > v = 4 \times \frac{22}{7} \times 7 \times 7$

$= > v = 88 \times 7 = 616 \: cm^{2}$

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