Multiple choice

10 spheres, each of radius 5 cm are melted and casted into cones of height 10 cm and radius of base as 5 cm. The number of such cones that can be casted from the metal is

  1. 20

  2. 15

  3. 10

  4. 22
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume is conserved when melting and recasting. Volume of 10 spheres = 10 × (4/3)πr³ = 10 × (4/3)π(5)³ = 10 × (500/3)π = (5000/3)π. Each cone volume = (1/3)πR²h = (1/3)π(5)²(10) = (250/3)π. Number of cones = (5000/3)π ÷ (250/3)π = 5000/250 = 20. Option A (20) is correct.

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