Question

Two spheres are having the ratio of their densities 1: 3 and masses in 3: 4 respectively. Find the ratio of their volumes.

Answer 1

$\frac{{\varrho }_1}{{\varrho }_2}=\frac{1}{3}\&\frac{m_1}{m_2}=\frac{3}{4}$

Since, $\varrho =\frac{mass}{volume}$

hence $\frac{m_1/v_1}{m_2/v_2}=\frac{{\varrho }_1}{{\varrho }_2}$

$\frac{1}{3}=\frac{m_1}{m_2}\times \frac{v_1}{v_2}$

$\frac{v_1}{v_2}=\frac{3}{4}\times 3=\frac{9}{4}$

$\frac{v_1}{v_2}=9/4$