3 solid spheres of diameters 6 cm, 8 cm and 10 cm are melted together to form a single solid sphere. Find its radius.

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Question

This question was previously asked in

SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 04 Jul, 2024 Shift 4)

Answer 1

Given:

Three solid spheres of diameters 6 cm, 8 cm, and 10 cm are melted to form a single solid sphere.

Formula used:

Volume of a sphere = \(\frac{4}{3}\pi r^3\)

The volume of the resulting sphere is equal to the sum of the volumes of the three smaller spheres.

Calculation:

Radius of the first sphere, r₁ = 6/2 = 3 cm

Radius of the second sphere, r₂ = 8/2 = 4 cm

Radius of the third sphere, r₃ = 10/2 = 5 cm

Volume of the resulting sphere = volume of first sphere + volume of second sphere + volume of third sphere

⇒ \(\frac{4}{3}\pi R^3\) = ⁴⁄₃π(3³) + ⁴⁄₃π(4³) + ⁴⁄₃π(5³)

⇒ R³ = 3³ + 4³ + 5³

⇒ R³ = 27 + 64 + 125

⇒ R³ = 216

⇒ R = 6 cm

∴ The correct answer is option (1).

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