Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am having a problem getting started on this problem.

Rate of inflation of a balloon. A spherical balloon is inflated at a rate of 10 cubic cm/min. At what rate is the diameter of the balloon increasing when the balloon has a diameter of 5 cm.

For the life of me I cannot figure out what formula to begin with so I can find dd/dt (this is an assumption that it is related to diameter) not sure it could be related to anything else. I am not looking for the problem to be solved just help getting started.

share|improve this question

2 Answers 2

up vote 0 down vote accepted

HINT: volume of the balloon($V$) = $\frac{4}{3}\pi r^3=\frac{4}{3}\pi {(\frac{D}{2})}^3=\frac{1}{6}\pi D^3$

and you are given $\frac{dV}{dt}$ and need to find $\frac{dD}{dt}$

share|improve this answer
    
thank you yes this helped. –  samack Sep 25 '12 at 4:01
    
@samack:i am glad :) –  Aang Sep 25 '12 at 4:02

We need a relationship between the diameter $x$ and the volume $V$. The standard formula for volume is $$V=\frac{4}{3}\pi r^3,$$ where $r$ is the radius. In terms of diameter, since $r=x/2$, we have $$V=\frac{\pi x^3}{6}.$$ It is I think best to differentiate immediately, using the Chain Rule. We get $$\frac{dV}{dt}=\frac{\pi x^2}{2}\frac{dx}{dt}.$$ Now can you finish?

share|improve this answer
    
thank you yes this helped –  samack Sep 25 '12 at 4:04

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.