24 equal solid hemispheres are melted to form a right circular cylinder of radius 12 cm and height 24 cm. Find the radius of each solid hemisphere.

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SSC CHSL Tier-I Exam 2022 Official Paper (Held On: 15 March, 2023 Shift 1)
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  1. 4 cm
  2. 8 cm
  3. 6 cm
  4. 3 cm

Answer (Detailed Solution Below)

Option 3 : 6 cm
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Detailed Solution

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Given:

Number of solid hemispheres = 24

Radius of the cylinder = 12 cm

Height of the cylinder = 24 cm

Formula used:

The volume of a hemisphere = (2/3)πr³

Calculation:

The total volume of the 24 solid hemispheres is equal to the volume of the cylinder.

Let's calculate the volume of the cylinder first using the formula:

The volume of the cylinder = πr²h

π(12 cm)² × 24 cm

144 × 24π

Since the 24 solid hemispheres have the same volume as the cylinder, the volume of each hemisphere can be calculated as: 

Now, equate the volume of 24 hemispheres to the cylinder.

24 × (2/3) πr³ = 144 × 24π

(2/3)r³ = 144

r3 = 216

r = 6

Therefore, the radius of each solid hemisphere is 6 cm.

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