Multiple choice

The height of a right circular cylinder is $6 m$. If three times the sum of the areas of its two circular faces is twice the area of the curved surface, then the radius of the base is

  1. $4 m$
  2. $3 m$
  3. $2 m$
  4. $1 m$
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A Correct answer
Explanation

Let r be the radius and h = 6. The area of two circular faces is 2 * pi * r^2. The curved surface area is 2 * pi * r * h. The problem states 3 * (2 * pi * r^2) = 2 * (2 * pi * r * 6). Simplifying gives 6 * pi * r^2 = 24 * pi * r. Dividing by 6 * pi * r (assuming r is not 0) gives r = 4.

AI explanation

The combined area of the two circular faces is 2 times pi times r squared, so three times this sum equals 6 times pi times r squared. The area of the curved surface is 2 times pi times r times h, and substituting height 6 gives 12 times pi times r. Setting the equation 6 times pi times r squared equal to twice 12 times pi times r yields 6 times pi times r squared equals 24 times pi times r, so r equals 4 m.

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