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.

R + R = 10

4/3 r³ π : 4/3 R³ π = 27 : 343

r ³ : R ³ = 27 : 343 / ∛

r : R = 3 : 7

3 R = 7 r

R = 7 r / 3

r + 7 r / 3 = 10 / · 3

3 r + 7 r = 30

10 r = 30

r = 30 : 10

r = 3

Answer: the radius of the smaller sphere is 3.