Multiple choice

A solid right circular cylinder of base radius 'p' and height 'h' is melted and recast into a sphere of radius 'q'. If h = q, then which of the following relationships is true?

  1. p2 = 2q2

  2. 3p2 = 4q2

  3. p2 = 2q

  4. p2 = 4q
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B Correct answer
Explanation

Volume of cylinder = pi*p^2*h. Volume of sphere = (4/3)*pi*q^3. Since h=q, pi*p^2*q = (4/3)*pi*q^3. Dividing by pi*q (assuming q is not 0), p^2 = (4/3)*q^2, which is 3p^2 = 4q^2.

AI explanation

When a cylinder is recast into a sphere, the volumes remain equal, so pi times p squared times h equals four-thirds times pi times q cubed. Given that h equals q, we substitute q for h to get pi times p squared times q equals four-thirds times pi times q cubed. Dividing both sides by pi times q leaves p squared equal to four-thirds times q squared, which simplifies to 3p2 = 4q2.

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