Two metallic right circular cones having heights 3.8 cm and 4.6 cm and radii of their bases 2.1 cm each, have been melted togethe…

Question

Two metallic right circular cones having heights 3.8 cm and 4.6 cm and radii of their bases 2.1 cm each, have been melted together and recast into a sphere. The diameter (in cm) of the sphere is:

1. A. 4.2 (Correct answer)
2. B. 1.4
3. C. 3.5
4. D. 6.3

Correct Answer

Option A — 4.2

Detailed Solution & Explanation

The correct answer is 4.2.

Key Points

• Total cone volume = (1/3)*pi*(2.1^2)*(3.8+4.6) = (1/3)*pi*(4.41)*(8.4) = 12.348*pi.
• (4/3)*pi*r^3 = 12.348*pi => r^3 = 9.261 => r = 2.1. Diameter = 4.2 cm.