How many spherical lead shots each of diameter 8.4 cm can be obtained from a rectangular solid of lead with dimension 88 cm, 63 cm, 42 cm,(take \(\pi= \frac{22}{7}\)) ?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 1)

Answer 1

Given:

Diameter of each lead shot = 8.4 cm

Dimension of the rectangular solid = 88 × 63 × 42 (cm)

Concept used:

1. Volume of a sphere = \(\frac {4\pi × (Radius)^3}{3}\)

2. Volume of a cuboid = Length × Breadth × Height

3. The collective volume of all lead shots obtained should be equal to the volume of the rectangular solid.

4. Diameter = Radius × 2

Calculation:

Let N number of shots can be obtained.

Radius of each lead shot = 8.4/2 = 4.2 cm

According to the concept,

N × \(\frac {4\pi × (4.2)^3}{3}\) = 88 × 63 × 42

⇒ N × \(\frac {4 × 22 × (42)^2}{3 × 7 × 1000}\) = 88 × 63

⇒ N = 750

∴ 750 lead shots can be obtained.

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