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 r2 h1 + (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.