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

Given is, two solid spheres of same metal. ⇒ Density of both spheres are same.

Mass (weight) of larger sphere, M = 5920 g

Mass (weight) of smaller sphere, m = 740 g

Diameter of smaller sphere = 5 cm

⇒ radius of smaller sphere, r = 5/2 = 2.5 cm

Volume of smaller sphere, v = 4/3 πr³

⇒

⇒ v = 1375/21 cm³

We know, density = mass/volume

⇒ density of smaller sphere = m/v

⇒ …(i)

And density of larger sphere = M/V

⇒ density of larger sphere = 5920/V g/cm …(ii)

By equations (i) & (ii), we get

Density of smaller sphere = Density of larger sphere

⇒

⇒

Volume of the larger sphere = 523.81 cm³

⇒ 4/3 πR³ = 523.81 [∵, volume of larger sphere = 4/3 πR³, where R = radius of the larger sphere]

⇒

⇒ R³ = 125

⇒ R = (125)^1/3

⇒ R = 5

Thus, radius of the larger sphere is 5 cm.