Q. 15.0( 1 Vote )

The surface area of a balloon being inflated, changes at a rate proportional to time t. If initially its radius is 1 unit and after 3 seconds it is 2 units, find the radius after time t.

Answer :

Let the surface area of the balloon be S.

S = 4πr2

According to the question,


8πrdr = ktdt

Integrating both sides, we have

8π∫rdr = k∫tdt


Given, we have r = 1 unit when the t = 0 sec

Putting the value in equation (1)

4π (1)2 = k × 0 + c

c = 4π ……(2)

Putting the value of c in equation (1) we have,


Given, we have r = 2 units when t = 3 sec


Now, putting the value of k in equation (2),

We have,

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