Question

The external radius of a hollow sphere made of lead sheet of 1 cm. thickness is 6cm. If melting the sphere, a solid right circular rod of 2cm. radius is made, then let us calculate the length of the rod.​

Answer 1

Answer:

The length of the circular rod = 30.33 cm

Step-by-step explanation:

Given:

• The external radius of a hollow sphere made of lead sheet of 1 cm thickness is 6 cm.
• Melting the sphere, a solid right circular rod of 2 cm radius is made.

To find:

• The length of the circular rod.

Solution:

Melting the sphere, a solid right circular rod is made, so from here we can state that,

Volume of a sphere = Volume of a cylinder

Using this and the formula of both respectively, we can easily find the height of the circular rod which is equal to the length of the circular rod.

♦ 4/3 π(R³ - r³) = π(r')² h

Here,

R = 6

r = 5

r' = 2

Further doing calculations,

• 4/3 × π × (6³ - 5³) = π × 2² × h
• 4/3 × (6³ - 5³) = 2² × h
• 4/3 × (6³ - 5³) = 4 × h
• 4/3 ÷ 4 × (6³ - 5³) = h
• 4/3 × 1/4 × (6³ - 5³) = h
• 1/3 × (6³ - 5³) = h
• 1/3 × (216 - 125) = h
• 1/3 × 91 = h
• h = 91/3
• h = 30.33 cm

∴ The length of the circular rod = 30.33 cm

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