The volume of spherical balloon being inflated changes at a const | Filo

Class 12

Math

Calculus

Differential Equations

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150

The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of balloon after t seconds.

Solution: Solution: Here, Volume is changing at a constant rate.
So, , where is a constant.
Now, Volume of a sphere,
So,

As,.So,

Now, integrating both sides,
->(1)
, where
So, at

At

Putting values of and in (1),

So, at any time radius of the baloon will be .
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