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

Question

mathmale · Answer

I'd suggest that you:
1.  Write out the formula for the volume of a sphere.
2.  Choose literals (letters) to represent the radius of the smaller and of the larger sphere, respectively.
3.  Write an equation showing how these two radii are related
4.  Use the given ratio to write an equation of ratios for the two volumes.
5.  solve that for either unknown.
6.  Find the other unknown.

tennistar · Answer

Wouldn't this be case of cross multiplying?

tennistar · Answer

And solving for x?

anonymous · Answer

$$((4/3)(\pi)(r _{b}))/ (4/3)\pi(r _{s}) = 37/343$$

Note also that $$r _{b} + r _{s} = 10$$

write the second formula in terms of another variable and plug it in the equation and solve the ratio for other radius. Hope this helped.

anonymous · Answer

sorry forget to put it, but the radius is cubed. Nice question btw.

anonymous · Answer

The ratio of the volumes is the cube of the ratio of radii so
$$
\frac {r^3}{R^3}=\frac {27}{343}=\frac {3^3}{7^3}\
\frac {r}{R} =\frac {3}{7}\
R+r=10
$$
Can you fin r and R

anonymous · Answer

It ssems to me obvious that r=3 and R=7