Multiple choice

A solid metallic sphere of radius x cm is melted and then drawn into 126 cones each of radius 3.5 cm and height 3 cm. There is no wastage of material in this process. What is the value of x?

  1. 10.5

  2. 7

  3. 3.5

  4. 21

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A Correct answer
Explanation

Volume of sphere = 126 * Volume of cone. (4/3) * pi * x^3 = 126 * (1/3) * pi * (3.5)^2 * 3. x^3 = 126 * (3.5)^2 * (3/4) = 126 * 12.25 * 0.75 = 1157.625. x = cuberoot(1157.625) = 10.5.

AI explanation

The volume of a sphere formula is (4/3) * pi * x^3 and the volume of one cone is (1/3) * pi * r^2 * h. Equating the sphere's volume to 126 cones gives (4/3) * pi * x^3 = 126 * (1/3) * pi * 3.5 * 3.5 * 3. Canceling pi and 3 leaves 4x^3 = 126 * 12.25, so x^3 = 1157.625 and x = 10.5 cm. The value of x is 10.5.