Multiple choice

The surface area of a cylinder is 33x2 square units. The sum of the radius and the height of the cylinder is 6x units. What is the circumference of the base of the cylinder, in units?

  1. 5.5x

  2. 8.5x

  3. 11x

  4. 12x
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A Correct answer
Explanation

The total surface area of a cylinder is given by the formula 2 * pi * r * (r + h), where r is the radius and h is the height. Substituting the given surface area of 33x^2 and the sum of the radius and height of 6x, we get 2 * pi * r * (6x) = 33x^2. Solving for the circumference, which is 2 * pi * r, yields 33x^2 / 6x = 5.5x.

AI explanation

Using the total surface area formula for a cylinder, 2 times pi times r times (h plus r) equals 33 times x squared. We are given that (h plus r) equals 6x, so substituting this into the area formula gives 2 times pi times r times 6x equals 33 times x squared. Simplifying this yields 12 times pi times r times x equals 33 times x squared, meaning pi times r equals 2.75x. Since the circumference of the base is 2 times pi times r, the circumference is 2 times 2.75x, which is 5.5x units.

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