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

Asked on by xdsmith

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jeew-m's profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

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` .


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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

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


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

=31 cm^3

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