Homework Help: Expanding surface of sphere

1. Aug 26, 2007

jackt

a spherical balloon expands when it is taken from the cold outdoors to the inside of a warm house. if its surface area increases 19.4%, by what percentage does the radius of the balloon change?

I've tried this several times but im not sure how to go about beginning the work

2. Aug 26, 2007

robphy

If I were doing this problem,
I would write down quantities with labels like:

for the volume of the ball before...
$$V_{before}=\frac{4\pi}{3}r_{before}^3$$
and, similarly, for "after".
They can be compared by taking the ratio:
$$\frac{ V_{after} }{V_{before} }$$.

How would you use this strategy with your particular problem?

What does "increases 19.4%" mean in terms of a ratio?

3. Aug 28, 2007

ron_jay

The increase in 19.4% means the difference between the new surface area and the original or we could write it as:

4(pi)R^2-4(pi)r^2 where R is the new(larger) radius and r the original radius

We also know that increase percentage is calculated on the original value which happens to be 4(pi)r^2.

Hence, {4(pi)R^2-4(pi)r^2}/4(pi)r^2 *100=19.4

Evaluate this and then find the relation only in terms of the ratio of the difference in radius to the original radius...

Last edited: Aug 28, 2007
4. Aug 28, 2007

robphy

For this type of problem, it's more efficient to think in ratios of radii, rather than difference in radii.