Question

I’ve tried solving this question but haven’t had any luck

Answer 1

The volume of balloon is given

`V(r)=(4)/(3)(\Pi)r^2`

It is also given that the radius is increasing over time with the relation r(t)=15t.

a. The volume in terms of time is

`(V\circ r)(t)=(4)/(3)(\Pi)(15t)^3=4*5*15*15(\Pi)t^3=4500(\Pi)t^3`

b. The volume is given 600,000 cubic inches. We have to determine the time in minutes.

`600,000=4500*(\Pi)* t^3`
`t^3=(600,000)/(4500*\Pi)=42.463`
`t=3.45\min`

Hence the time in minutes is 3.45 min.