Multiple choice

The volume of a right circular cylinder is the same numerical value as its total surface area. Find the smallest integral value for the radius of the cylinder.

  1. 1

  2. 2

  3. 3

  4. 4

  5. This value cannot be determined.
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C Correct answer
Explanation

Volume of cylinder = pi * r^2 * h. Total surface area = 2 * pi * r * h + 2 * pi * r^2. Setting them equal: pi * r^2 * h = 2 * pi * r * (h + r). r * h = 2 * (h + r). r * h = 2h + 2r. h(r - 2) = 2r. h = 2r / (r - 2). For h > 0, r must be > 2. The smallest integer r > 2 is 3.

AI explanation

Equating the volume and total surface area formulas gives ^2*h = 2 r(r+h). Dividing both sides by r leaves h = 2 (r+h), which simplifies to h = 2r. Substituting this back into the surface area equation yields ^2(2r) = 2 r(r+2r), meaning 2 ^3 = 6 ^2, so r = 3.

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