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Q58 (CAPF/2026) Science & Technology › Basic Science (Physics, Chemistry, Biology)

A metallic cylindrical disc of radius 7 cm is melted and 22 square-shaped solids of the same thickness are made. If l cm is the side length of these squares, then (in cm)

Result
Your answer: —  ·  Correct: B

Explanation

The volume of a metallic cylindrical disc is calculated using the formula V = πr2t, where r is the radius and t is the thickness. Given r = 7 cm, the volume is π × 72 × t.

This disc is melted to form 22 square-shaped solids of the same thickness t and side length l. The volume of one such square solid is l2t. Thus, the total volume of 22 solids is 22 × l2t.

Since the total volume remains constant during the melting process:
π × 72 × t = 22 × l2 × t
(22/7) × 49 = 22 × l2 (Cancelling t and substituting π ≈ 22/7)
22 × 7 = 22 × l2
l2 = 7
l = √7

We know that 2.62 = 6.76 and 2.72 = 7.29. Therefore, √7 lies between 2.6 and 2.7 (√7 ≈ 2.646). This corresponds to the range 2.6 < l < 2.7. Option B is the correct match.

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