# A balloon is inflated so that its increase in volume is at a constant rate of 10cm^3 s^-1. if its volume is initially 1 cm^3, find its volume after 3 sec ans:31 cm3

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Let volume of the balloon at any time t sec be V cm^3.

We have given

`(dV)/(dt)=10 `

`dV=10 dt`

``on integration

V=10t+c

where c is constant to be determined.

But initial condition is t=0 then V=1 cm^3

1=10 x 0+c

c=1

Thus

V=10t+1

so volume after 3 second

V=10 x 3+1

=31 cm^3

Initial volume `= 1cm^3`

Rate of volume increase `= 10(cm^3)/s`

So with in 3 seconds the volume will increase by `10xx3 = 30cm^3`

Since the initial volume is `1cm^3` ;

Final volume of the balloon `= 30+1 = 31cm^3`

*So the answer is `31cm^3` .*