Question

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

Options

• 19 cm

• 21 cm

• 23 cm

• 25 cm

Answer 1

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

Explanation:

Volume of the cuboid  = (l × b × h) = 49 × 33 × 24 cm³

Let the radius of the sphere`=4/3` 

The volume of the sphere and the cuboid are the same.

Therefore,

`4/3 pi"r"^3 = l × b × h`

`=> 4/3xx22/7xx"r"^3=49xx33xx24`

`=> "r"^3 = 49xx33xx24xx21/88`

`=> "r"^3 = 21xx21xx21`

`=> "r"^3 = (21)^3` 

⇒ r = 21 cm

Hence, the radius of the sphere is 21 cm.