Question

A solid piece of iron in the form of a cuboid of dimensions 49 cm × 33 cm × 24 cm, is moulded to form a solid sphere. The radius of the sphere is ______.

Options

• 21 cm

• 23 cm

• 25 cm

• 19 cm

Answer 1

A solid piece of iron in the form of a cuboid of dimensions 49 cm × 33 cm × 24 cm, is moulded to form a solid sphere. The radius of the sphere is 21 cm.

Explanation:

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 = `4/3 pir^3`

Where r = radius of sphere

Also, volume of cuboid = volume of sphere molded

So, 49(33)(24) = `4/3 pir^3`

⇒ πr³ = 29106

⇒ r³ = `29106 xx 22/7`

⇒ r³ = 9261

⇒ r = `root(3)(9261)` cm = 21 cm

Hence, radius of sphere is 21 cm