Question

if the ratio of radii of 2 spheres is 2:3 then find the ratios of their volumes

Answer 1

Radii of two sphere be r₁ and r₂ is 2:3.

Let the radii's be 2x and 3x.

Ratio of their volumes = $\frac{{\displaystyle \frac{4}{3}}\pi r_1^3}{\frac{4}{3}\pi r_2^3}=\frac{{\displaystyle r_1^3}}{r_2^3}=\frac{{\left(2x\right)}^3}{{\left(3x\right)}^3}=\frac{8x^3}{27x^3}=\frac{8}{27}\mathrm{or}8:27$