Question

g You are blowing air into a spherical balloon at a rate of 33 cubic inches per second. Given that the radius of the balloon is 22 inches when t=4t=4 seconds answer the following questions: (a) How fast is the radius of the balloon growing at t=4t=4 seconds

Answer 1

Answer:

$\frac{3}{16\pi}in/sec$

Explanation:

We are given that

$\frac{dv}{dt}=3in^3/s$

r=2 in when t=4 s

We have to find the rate of change of radius.

We know that

Volume of sphere=$V=\frac{4}{3}\pi r^3$

Differentiate w.r.t t

$\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$

Substitute the values

$3=4\pi(2)^2\times \frac{dr}{dt}$

$\frac{dr}{dt}=\frac{3}{4\pi(2)^2}$

$\frac{dr}{dt}=\frac{3}{16\pi}in/sec$