Question

If the ratio of two spheres 2:3 find the ratio of their volumes.

Answer 1

so the ratio of radius is 2:3

so volume of sphere  $\frac{4}{3}$πr³

so let the radius of sphere 1 and 2 be r₁ and r₂ respectively


so the ratio is $\frac{V_1}{V_2}=\frac{\frac{4}{3} \pi r_1^3}{\frac{4}{3} \pi r_2^3}$

so   $\frac{V_1}{V_2}=\frac{r_1^3}{r_2^3}$

⇒  $\frac{V_1}{V_2}=\frac{8}{27}$   ANSWER

Answer 2

If the ratio of the radii of two spheres is x : y then the ratio of their volumes is x³ : y³

If the ratio of radii is 2 : 3 then the ratio of volumes is 8 : 27