Two spheres made of different materials but having the same mass, hace radii in the ratio of 3 : 4. Find the ratio of their densities.

Explanation

Volume of sphere, V =` (4)/(3)pir^(3)`
Density of substance =` ("mass of substance")/("volume of the substance")`
When the mass ofk two spheres are same then the ratio of densities, `(D_(1))/(D_(2))= (V_(2))/(V_(1))` `(therefore mass of equal)`
The ratio of radi of the two spheres = `(r_(1))/(r_(2))=(3)/(4)`
Then, the ratio of then volumes = `(V_(1))/(V_(2))= ((4)/(3)pir_(1)^(3))/((4)/(3)pir_(2)^(3))`
`rArr V_(1)/V_(2)=(r_(1)^(3))/(r_(2)^(3))= 3^(3)/4^(3)=(27)/(64)`
Then, the ratio of densities of the two spheres
= `D_(1)/D_(2)=V_(2)/V_(1)rArr D_(1)/D_(2)=(64)/(27)`