Q2 (CISF/2021) Science & Technology › Basic Science (Physics, Chemistry, Biology)

A solid metal ball of diameter 10 cm is melted and cast into smaller balls of diameter 1 cm. How many such small balls can be made ?

Result

Your answer: — · Correct: C

Explanation

The volume of a sphere is calculated using the formula V = ⁴⁄₃πr³, where r is the radius. When a solid object is melted and recast into new shapes, the total volume remains conserved.

Given:
Diameter of large ball = 10 cm, so Radius (R) = 5 cm.
Diameter of small ball = 1 cm, so Radius (r) = 0.5 cm.

The number of small balls (n) is determined by dividing the total volume of the large ball by the volume of a single small ball:
n = (⁴⁄₃πR³) ÷ (⁴⁄₃πr³)
n = R³ ÷ r³ = (R/r)³
n = (5 ÷ 0.5)³ = 10³ = 1000.

Hence, 1000 such small balls can be made from the larger sphere.

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A solid metal ball of diameter 10 cm is melted and cast into smaller balls of diameter 1 cm. How many such small balls can be made ?

Explanation

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