Question

28. The diameter of a metallic sphere is equal to 9 cm. It is melted and drawn into a long wire
of diameter 2 mm having uniform cross-section. Find the length of the wire.​

Answer 1

Answer:

Step-by-step explanation:

Diameter of the metallic sphere = 9 cm

Radius of the metallic sphere , r = 9/2 cm = 4.5 cm

Volume of the metallic sphere = 4/3 × πr³

Diameter of the cylindrical wire = 2 mm = 2/10 cm = 0.2 cm

Radius of the cylindrical wire , r1 = 0.2/2 cm = 0.1 cm

Let the height of the cylindrical wire = h cm

Volume of the cylindrical wire = πr1²×h

Volume of the metallic sphere = Volume of the cylindrical wire

4/3 × πr³ = πr1²×h

4/3 × π  × 4.5³ = π(0.1)²×h

4/3 × 4.5 × 4.5 × 4.5 = 0.01h

4 × 1.5 ×  4.5 × 4.5 = 0.01 × h

h = (4 × 1.5 ×  4.5 × 4.5)/0.01

h = 121.5/0.01 = 121.5 × 100 = 12150 cm

h = 12150 cm  

Hence, the required length of the wire is 12150 cm.

Answer 2

Step-by-step explanation:

SOLUTION ✍️

____'________________

Step-by-step explanation:

Diameter of the metallic sphere = 9 cm

Radius of the metallic sphere , r = 9/2 cm = 4.5 cm

Volume of the metallic sphere = 4/3 × πr³

Diameter of the cylindrical wire = 2 mm = 2/10 cm = 0.2 cm

Radius of the cylindrical wire , r1 = 0.2/2 cm = 0.1 cm

Let the height of the cylindrical wire = h cm

Volume of the cylindrical wire = πr1²×h

Volume of the metallic sphere = Volume of the cylindrical wire

4/3 × πr³ = πr1²×h

4/3 × π  × 4.5³ = π(0.1)²×h

4/3 × 4.5 × 4.5 × 4.5 = 0.01h

4 × 1.5 ×  4.5 × 4.5 = 0.01 × h

h = (4 × 1.5 ×  4.5 × 4.5)/0.01

h = 121.5/0.01 = 121.5 × 100 = 12150 cm

h = 12150 cm  

Hence, the required length of the wire is 12150 cm.

hope this helps you!!