Question

Tow solid spheres made of the same metal have weight 5920 g and 740 g, resopectively. Determine the radius of the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

Answer 1

Teo solid sphere madeof the same metal have weight 5920 g and740 g, respectively. Mass per unit volume is called the density.
`therefore (V_(1))/(V_(2))=((5920)/(D))/((740)/(D)) rArr ((4)/(3)pi r_(1)^(3))/((4)/(3)pi r_(2)^(3))=(5920)/(740)`
`rArr (r_(1)^(3))/(r_(2)^(3))=(5920)/(740) rArr (r_(1)^(3))/(((5)/(2))^(3))=(5920)/(740) " " [because r_(2)=(1)/(2)xx5]`
`rArr r_(1)^(3)=(5920)/(740)xx(125)/(8)=125 rArr r_(1)=(12.5)^(1//3)=5cm`
Hence, the radiusof the larger sphere = 5 cm.