Two solid spheres made of the same metal havemasses of 5920 g and 740 g respectively. Determinethe radius of the larger sphere, if the diameter of the smaller sphere is 5 cm.

Two solid spheres made of the same metal havemasses of 5920 g and 740

1.	Two solid spheres made of the same metal havemasses of 5920 g and 740 g respectively. Determinethe radius of the larger sphere, if the diameter of the smaller sphere is 5 cm.
Answer» Given :- Weight of the heavier sphere = 5920 g and weight of the lighter sphere = 740 g, and diameter of lighter sphere = 5 cm or radius = 2.5 cmLet the volume of the heavier sphere be 'V1' and the volume of the lighter sphere be 'V2'. Radius of the heavier sphere be 'r1' because the diameter of the lighter sphere is given so the radius is 2.5 cm.Weight of an object = density× volume of that objectSo,(Weight of the heavier sphere/weight of the lighter sphere) = (Density× V1/density× V2)As both the spheres are made up of same metal, therefore, the ratio of their weights will be equal to the ratio oftheir volumes.(weight of the heavier sphere/weight of the lighter sphere) = (V1/V2)⇒ (5920/740) = (4/3πr₁³)/(4/3πr³)⇒ (5920/740) = (4/3×22/7×r₁³)/(4/3× 22/7× 2.5× 2.5× 2.5)⇒ 8 = r₁³× 1/2.5× 1/2.5× 1/2.5⇒ 8 = r₁³× 1/15.625⇒ r₁³ = 8× 15.625⇒ r₁³ = 125⇒r₁ = 5 cmSo, the radius of the heavier sphereis 5 cm.Answer.