1.

Find the number of lead balls, each with a diameter of 3 cm, that can be made from a sphere of diameter 21 cm.1. 1962. 2163. 2564. 343

Answer» Correct Answer - Option 4 : 343

Given:

Diameter of sphere = 21 cm

Diameter of lead balls = 3 cm

Formula used:

Volume of sphere = 4/3(πr3)

Calculation:

Let ‘n’ be the number of lead balls that can be made from a sphere

Radius of sphere = 21/2 cm

Radius of lead balls = 3/2 cm

⇒ Volume of sphere = 4/3(πr3)

⇒ Volume of sphere = 4/3[π(21/2)3]

⇒ Volume of lead ball = 4/3[π(3/2)3]

According to the question,

Volume of sphere = n × Volume of lead balls

⇒ 4/3[π(21/2)3] = n × 4/3[π(3/2)3]

⇒ (21/2)3 = n × (3/2)3

⇒ 9261/8 = n × 27/8

⇒ n = 9261/27

⇒ n = 343 

∴ The number of lead balls, each with a diameter of 3 cm, that can be made from a sphere of diameter 21 cm is 343.


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