Question

The largest possible sphere is carved out of a wooden solid cube of side 7 cm. Find the volume of the wood left. (Use$(\pi=\frac{22}{7})$).

Answer 1

Answer:

The volume of wood left is 163.33 cm³.

Step-by-step explanation:

SOLUTION :  

Given :  

Side of cube =  7cm

Diameter of sphere = Side of cube =  7cm

Radius of sphere = side of cube/2 = 7/2 = 3.5 cm

Volume of wood left = Volume of Cube - Volume of sphere

= Side³ - 4/3πr³

= 7³ - 4/3 × 22/7 × 3.5³

= 343 - 4/3 ×(22/7)×(3.5)×(3.5)×(3.5)

= 343 - 4/3 × 22×(0.5)×3.5×3.5

= 343 - 179.67

Volume of wood left = 163.33 cm³

Hence, the volume of wood left is 163.33 cm³.

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Answer 2

Answer:

Diameter of Sphere = Side of cube = 7 cm

Hence, radius of sphere =

2

7

cm

Volume of wood left = Volume of cube - volume of sphere

= s

3

−

3

4

πr

3

= 7×7×7−

3

4

×

7

22

×

2

7

×

2

7

×

2

7

= 343−

3

539

=

3

490

= 163.33cm