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
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` .
Let volume of the balloon at any time t sec be V cm^3.
We have given
where c is constant to be determined.
But initial condition is t=0 then V=1 cm^3
1=10 x 0+c
so volume after 3 second
V=10 x 3+1