Multiple choice

Mark the correct alternative of the following. A cylinder with radius r and height h is closed on the top and bottom. Which of the following expressions represents the total surface area of this cylinder?

  1. $2\pi r(r+h)$
  2. $\pi r(r+2h)$
  3. $\pi r(2r+h)$
  4. $2\pi r^2+h$
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A Correct answer
Explanation

Total surface area of a cylinder = lateral area + 2 * base area = 2 * pi * r * h + 2 * pi * r^2 = 2 * pi * r * (h + r).

AI explanation

The total surface area of a closed cylinder is the sum of its curved surface area and the areas of its two circular bases. The curved surface area is 2*pi*r*h, and the area of the two bases is 2*pi*r^2. Factoring out 2*pi*r gives the combined formula 2*pi*r*(r + h).

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