Multiple choice

A solid metallic sphere of radius 6.3 cm is melted and recast into a right circular cone of height 25.2 cm. What is the ratio of the diameter of the base to the height of the cone?

  1. 2 : 1

  2. 3 : 2

  3. 1 : 2

  4. 2 : 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of sphere = (4/3)pi*r^3 = (4/3)*pi(6.3)^3. Volume of cone = (1/3)pi*R^2*h = (1/3)*pi*R^2(25.2). Equating volumes: 4*(6.3)^3 = R^2*(25.2). Solving for R: R^2 = (4 * 6.3 * 6.3 * 6.3) / 25.2 = 6.3 * 6.3, so R = 6.3. The diameter is 2*R = 12.6. The ratio of diameter to height is 12.6 / 25.2 = 1/2.

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