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A balloon which always remains spherical is being inflated by pumping in gas at the rate of 900 cm3/sec. Find the rate at which the radius of the balloon is increasing when the radius of the balloon is 15 cm.

A balloon which always remains spherical is being inflated by pumping in gas at the rate of 900 cm3/sec. Find the rate at which the radius of the balloon is increasing when the radius of the balloon is 15 cm.

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
Let r and V be varaibles for radius and volume respectively
(dv/dt)=900
v=(4/3)\pi r^{3}
(dv/dt)=4\pi r^{2}(dr/dt)
dr/dt=(dv/dt)/4\pi r^{2}=(900)/4\pi(15)(15)
so dr/dt=(1/\pi) cm/sec
Thanks and Regards
Shaik Aasif
askIITians faculty

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