A ballon which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate of which the radius of the balloon is increasing when the radius is 15 cm.

Solution

Let r be the radius of the ballon and V be its volume at any time t. Then
$therefore space space space straight V space equals space 4 over 3 πr cubed space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space space space dV over dt space equals 4 over 3 straight pi. space space 3 straight r squared space dr over dt space equals space 4 πr squared space dr over dt$
But $dV over dt space equals space 900 space cm squared divided by straight s$ (given)
$therefore space space space space 4 πr squared space dr over dt space equals space 900 space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space space space dr over dt space equals space 225 over πr squared When space straight r space equals space 15 comma space space space dr over dt space equals space fraction numerator 225 over denominator straight pi space cross times space left parenthesis 15 right parenthesis squared end fraction space equals space 1 over straight pi space cm divided by straight s. therefore space space space radius space of space the space balloon space is space increasing space at space the space rate space of space 1 over straight pi space cm divided by straight s space when space the space radius space is space 15 space cm.$

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Application Of Derivatives

A ballon which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate of which the radius of the balloon is increasing when the radius is 15 cm.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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