Question

The largest sphere is carved out of a cube of wood of side 21 cm. Find the volume of remaining wood. (Hint :-diameter of sphere is 21 cm)

Answer 1

Given:
Side of a cube= 21 cm

Diameter of sphere= 21cm
Radius of sphere= 21/2 cm

Volume of remaining wood = vol. Of cube - vol. Of sphere

= Side³ - 4/3πr³

= 21³ - (4/3 )×( 22/7) × (21/2)³

= 21³ - (11×21×21)

= 21²( 21 -11)

= 441 × 10

= 4410 cm³

Hence, the volume of remaining wood = 4410 cm³

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Hope this will help you....

Answer 2

Solution :-

Each edge of the cube = 21 cm

Volume of the cube = Edge*Edge*Edge

⇒ 21*21*21

= 9261 cm³

Diameter of the sphere = 21 cm

Then, Radius = 21/2 = 10.5 cm

Volume of the sphere = 4/3*πr³

⇒ 4/3*22/7*10.5*10.5*10.5

⇒ 4851 cm³

Volume of the remaining wood = Volume of the cube - Volume of the sphere

⇒ 9261 cm³ - 4851 cm³

⇒ 4410 cm³

So, Volume of the remaining wood is 4410 cm³.

Answer.