Question

The total volume of two spheres is 10π cubic units. The ratio of the

areas is 4:9. What is the volume of the smaller sphere in cubic units

Answer 1

if you compare to the radius, the area goes with the square and the volume goes with the cube

Answer 2

\[\frac{\text{small area}}{\text{large area}}=\frac{4}{9}\] and therefore
\[\frac{\text{small radius}}{\text{large radius}}=\frac{2}{3}\]

Answer 3

finally
\[\frac{\text{small volume}}{\text{large volume}}=\frac{2^3}{3^3}\]