A sphere of diameter 20 cm made of metal A weighs 16 kg, while another sphere of diameter 30 cm made of metal B weighs 10 kg. What is the weight of a sphere of diameter 60 cm, which is made up of equal volume of metal A and B?

A sphere of diameter 20 cm made of metal A weighs 16 kg, while another sphere of diameter 30 cm made of metal B weighs 10 kg. What is the weight of a sphere of diameter 60 cm, which is made up of equal volume of metal A and B? Correct Answer 256 kg

Given,

Diameter of sphere made of metal A = 20 cm

Weight of sphere made of metal A = 16 kg

Diameter of sphere made of metal B = 30 cm

Weight of sphere made of metal B = 10 kg

As we know,

Volume of sphere = (4/3)π × (radius)³ = (π/6) × (diameter)³

⇒ Volume of sphere of metal A = (π/6) × (20)³ = (4000π/3) cm³

This means that weight of (4000π/3) cm³ of metal A = 16 kg

⇒ Weight of 1 cm³ of metal A = (3/4000π) × 16 = (3/250π) kg

Similarly,

⇒ Volume of sphere of metal B = (π/6) × (30)³ = (4500π) cm³

This means that weight of (4500π) cm³ of metal B = 10 kg

⇒ Weight of 1 cm³ of metal B = (1/4500π) × 10 = (1/450π) kg

Now,

Diameter of sphere made of both metals = 60 cm

⇒ Volume of sphere made of both metals = (π/6) × (60)³ = (36000π) cm³

∵ It is made up of equal volumes of both metals

⇒ Volume of metal A in the sphere = Volume of metal B in the sphere = 36000π/2 = 18000π cm³

⇒ Weight of 18000π cm³ of metal A = (3/250π) × 18000π = 216 kg

⇒ Weight of 18000π cm³ of metal B = (1/450π) × 18000π = 40 kg

∴ Weight of sphere of diameter 60 cm = 216 + 40 = 256 kg