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Two metallic cones of heights 4.1 cm and 4.3 cm and each radius of base radius as 2.1 cm are melted together and recast into a sphere. The diameter of the sphere in cm is
1. 4.2
2. 4.5
3. 4.8
4. 5

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Correct Answer - Option 1 : 4.2

Given:

Two metallic cones of heights 4.1 cm and 4.3 cm and each radius of base radius as 2.1 cm are melted together and recast into a sphere.

Formula used:

Volume of cone = (1/3)π r2h

Volume of sphere = (4/3)π r3

Calculation:

According to the question,

⇒ (1/3)π rh1 + (1/3)π r2 h2 = (4/3)π R3

⇒ (1/3)π (2.12 × 4.1 + 2.12 ×4.3) = (4/3)π R3

⇒ R3 = 37.044/4

⇒ R = ∛9.261 

⇒ R = 2.1 cm

⇒ Diameter = 2 R = 2 × 2.1

⇒ 4.2 cm

∴ The diameter of the sphere is 4.2 cm.

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