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Question
A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.
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Solution
Let the volume of the sun = V and radius = r
`therefore V = 4/3 pir^3`
`therefore (dV)/(dr) = 4/3 pi xx 3 r^2 = 4 pir^2`
`(dV)/(dr) = 4pi xx 10 xx 10` ...[∴ r = 10 cm]
= 400 `pi` cm3/s
Thus, when the radius is 10 cm, the volume of the balloon increases at a rate of 400 π cm2/s.
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