Multiple choice

How many cones (r = 3.5 cm : h = 3 cm) can be made by melting a sphere of radius 10.5 cm?

  1. 126

  2. 123

  3. 127

  4. 214

  5. 225
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A Correct answer
Explanation

Volume of sphere = (4/3)*pi*10.5^3. Volume of cone = (1/3)*pi*3.5^2*3. Number of cones = ((4/3)*pi*10.5^3) / ((1/3)*pi*3.5^2*3) = (4 * 10.5^3) / (3.5^2 * 3) = (4 * 1157.625) / 36.75 = 4630.5 / 36.75 = 126.

AI explanation

The volume of the sphere is 4 thirds pi times 10.5 cubed. The volume of one cone is one third pi times 3.5 squared times 3. The number of cones is the volume of the sphere divided by the volume of one cone. This gives 126.

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