If a solid piece of iron in the form of a cuboid of dimensions is moulded to form a solid sphere. Then, radius of the sphere is

Question

Philoid · Accepted Answer

As we know,

Volume of cuboid = lbh

where, l = length, b = breadth and h = height

For given cuboid,

Length, l = 49 cm

Breadth, b = 33 cm

Height, h = 24 cm

Volume of cube = 49×(33) × (24) cm³

Now,

Let the radius of cube be r.

As volume of sphere

where r = radius of sphere

Also,

Volume of cuboid = volume of sphere moulded

⇒

⇒ πr³ = 29106

⇒

⇒ r = ∛ 9261 cm = 21 cm

Hence, radius of sphere is 21 cm