A metallic solid cuboid of sides 44 cm, 32 cm and 36 cm melted and converted into some number of spheres of radius 12 cm. How many such sphere can be made with the metal (π = 22/7)?
1. 5
2. 6
3. 7
4. 8
A metallic solid cuboid of sides 44 cm, 32 cm and 36 cm melted and converted into some number of spheres of radius 12 cm. How many such sphere can be made with the metal (π = 22/7)?
1. 5
2. 6
3. 7
4. 8
1. 5
2. 6
3. 7
4. 8
Correct Answer – Option 3 : 7
Given:
The sides of the cuboid are 44 cm, 32 cm, and 36 cm
The radius of the sphere is 12 cm
Concept Used:
The volume of a cuboid of sides l, b and h = l × b × h
The volume of the sphere of radius r = (4/3)πr3
Calculation:
The volume of the metallic cuboid is (44 × 32 × 36) cm3
The volume of the sphere is (4/3) × π × 123
Let, the total number of such sphere is n
Accordingly,
44 × 32 × 36 = n × (4/3) × π × 123
⇒ 44 × 32 × 36 = n × (4/3) × (22/7) × 12 × 12 × 12
⇒ n = 44 × 32 × 36 × (3/4) × (7/22) × (1/12) × (1/12) × (1/12)
⇒ n = 7
∴ Such 7 spheres can be made by given metallic cuboid.