Multiple choice

A solid metallic cone of height 20 cm and base radius 15 cm is melted to make spherical balls, each of radius 5 cm. How many such balls can be made?

  1. 10

  2. 9

  3. 5

  4. 7

  5. 6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of cone = (1/3) * pi * 15^2 * 20 = 1500 * pi. Volume of sphere = (4/3) * pi * 5^3 = (500/3) * pi. Number of balls = (1500 * pi) / ((500/3) * pi) = 1500 * 3 / 500 = 9.

AI explanation

The volume of the solid metallic cone is found using the formula (1/3)*pi*r^2*h, which equals (1/3) * pi * 15^2 * 20 = 1500*pi cubic centimetres. The volume of one spherical ball is (4/3)*pi*r^3, calculated as (4/3) * pi * 5^3 = (500/3)*pi cubic centimetres. Dividing the total volume of the cone by the volume of a single ball gives 1500*pi divided by (500/3)*pi, which equals 9 balls.

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