A solid piece of iron in the form of a cuboid of dimensions 49cm × 33

1.	A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is(A) 21cm (B) 23cm (C) 25cm (D) 19cm
Answer» (A) 21cm 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 πr³ Where r = radius of sphere Also, Volume of cuboid = volume of sphere molded So, 49(33)(24) = 4/3 πr³ ⇒ πr³ = 29106 ⇒ r³ = 29106 × 22/7 ⇒ r³ = 9261 ⇒ r = ∛ 9261 cm = 21 cm Hence, radius of sphere is 21 cm

A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is(A) 21cm (B) 23cm (C) 25cm (D) 19cm

Answer»

(A) 21cm

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 πr³

Where r = radius of sphere

Also,

Volume of cuboid = volume of sphere molded

So,

49(33)(24) = 4/3 πr³

⇒ πr³ = 29106

⇒ r³ = 29106 × 22/7

⇒ r³ = 9261

⇒ r = ∛ 9261 cm = 21 cm

Hence, radius of sphere is 21 cm