Question

The ratio of the volumes of the two spheres is 27:343 and the sum of their radii is 10. Find the radius of the smaller sphere.

Answer 1

do you know if similar shapes have dimensions (example, length or radius) in the ratio a/b
then their surface area will be (a/b)^2 and the ratio of their volume will be (a/b)^3

Answer 2

We can solve this without the information about the sum of the radiuses being 10

Answer 3

Any two spheres are similar.
The cube of the ratio of the radii will be equal to the ratio of the volumes.
If x is one radius, then 10 -x is the other.

( x/(10-x))^3 = 27/343 ---> solve for x @rmgabriel

Answer 4

The radius of the smaller sphere, x, appears to be 3. That would give the larger sphere a radius of 7.

http://www.wolframalpha.com/input/?i=+%28+x%2F%2810-x%29%29%5E3+%3D+27%2F343