0

I just wanted to check to see if I answered this question correctly :) any help would be much appreciated

Q. Air is pumped into a spherical balloon such that the volume of the balloon is increasing at a rate of 3cm^2cm/sec.

(i)Find the rate of change of the radius of the balloon , when the radius is 7cm.Leave your answer in terms of PI.

(ii)Find the rate of change of the surface area of the balloon when the radius is 9cm

What I did:

(i) I differentiated the volume of a sphere to get dv/dt= 4πr^2 . I then subbed 7 in for r and the answer I got was 196π.

(ii) I differentiated the surface area of a sphere which gave me an answer of 8πr.I then subbed in 9 for r and I got 72π as my answer.

user912758
  • 27
  • Welcome to MSE. Please use MathJax to format your posts. To begin with, surround math expressions (including numbers) with $ signs and use _ for subscripts. $x_1$ comes out as $x_1$. As to the question, no you're not doing it correctly. The rate of change of the volume is always $3$, no matter what the radius. We are given the rate of change as cm$^2$ per second, which means that the independent variable is time. – saulspatz May 08 '21 at 16:39

1 Answers1

0

We are asked for the rate of change of the radius, that is for $\frac{dr}{dt}$. We have $$3=\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$$ using $$\frac{dV}{dt}=\frac{dV}{dr}\frac{dr}{dt}$$

Can you finish it now?

saulspatz
  • 53,131