Question

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

Answer 1

The volume of balloon is given

$V(r)=\frac{4}{3}(\Pi)r^2$

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

$(V\circ r)(t)=\frac{4}{3}(\Pi)(15t)^3=4\times5\times15\times15(\Pi)t^3=4500(\Pi)t^3$

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

$600,000=4500\times(\Pi)\times t^3$$t^3=\frac{600,000}{4500\times\Pi}=42.463$$t=3.45\min$

Hence the time in minutes is 3.45 min.