Multiple choice

A sphere of radius 5 cm is melted to form a cone with base of same radius. The height (in cm) of the cone is

  1. 5

  2. 10

  3. 20

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

Volume of sphere = 4/3 * pi * r^3 = 4/3 * pi * 125 = 500/3 * pi. Volume of cone = 1/3 * pi * r^2 * h = 1/3 * pi * 25 * h = 25/3 * pi * h. Equating volumes: 500/3 * pi = 25/3 * pi * h => 500 = 25h => h = 20.

AI explanation

Because the sphere is melted to form the cone, the volume is conserved, meaning the volume of the sphere equals the volume of the cone. Using the formula four-thirds multiplied by pi and the cube of the radius for the sphere gives a volume of 500 multiplied by pi divided by 3. The volume of the cone formula is one-third multiplied by pi, the square of the radius and the height; equating the two formulas gives 500 equals the square of 5 multiplied by the height. Solving this equation shows the height is 20 centimeters.

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