Multiple choice

A right circular cylinder and a right circular cone have equal base and bases and equal heights If their curved surfaces are in the ratio $8 : 5$, what is ratio of their base is to their heights ?

  1. $3:4$
  2. $5:4$
  3. $6:7$
  4. $9:8$
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A Correct answer
Explanation

The cylinder's curved surface area is 2πrh, and the cone's is πrl. Thus, 2h:l = 8:5, so l = 5h/4. Using l^2 = r^2 + h^2 gives r:h = 3:4.

AI explanation

The curved surface area of a cylinder is 2 times pi times r times h and for a cone is pi times r times the square root of r squared plus h squared. Taking their ratio and setting it to 8 over 5 gives 2 divided by the square root of r squared plus h squared equals 8 over 5. Solving this equation gives the square root of r squared plus h squared equals 5h over 4. Squaring both sides and solving yields the ratio of the base to the height is 3 to 4.

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