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The air if filled in a balloon and the v...

The air if filled in a balloon and the volume of balloon increases gradually. Find the rate of increase of volume of balloon with radius when of balloon becomes 30 cm.

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Here radius of balloon r = 30 cm
Volume of balloon, `V =(4)/(3)pi r^3`
Rate of increase of volume of balloom w.r.t radius
`(dV)/(dt) = (d)/(dr) ((4)/(3) pi r^3) = (4)/(3) pi xx3r^2 = 4pi r^2`
When r =30 cm = 0.30m
`(dV)/(dr) = 4xx(22)/(7)xx(0.30)^2 = 1.13 m^2`
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