Multiple choice

A cylindrical-shaped water tank has the sum of its radius and height equal to 26 units. Additionally, the curved surface area of the tank is 2,772 square units less than the total surface area. Find the total surface area of the cylindrical-shaped water tank.

  1. 660 square units

  2. 2,772 square units

  3. 3,076 square units

  4. 3,432 square units

  5. 3,626 square units
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D Correct answer
Explanation

The difference between the total surface area and the curved surface area of a cylinder is the area of its two circular bases, which is 2 * pi * r^2. Setting this equal to 2,772 gives r = 21. Since the sum of the radius and height is 26, the total surface area is 2 * pi * r * (r + h) = 2 * (22/7) * 21 * 26 = 3,432 square units.

AI explanation

The difference between the total surface area and the curved surface area of a cylinder is the area of its two circular bases, given by the formula 2 times pi times r squared. Setting this equal to 2,772 gives 2 times (22 divided by 7) times r squared equals 2,772. Solving for r squared gives 441, so the radius is 21 units. Since the sum of the radius and height is 26, the height is 5 units, making the total surface area 2 times pi times 21 times (21 plus 5) equal to 3,432 square units.

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