GED Mathematical Reasoning TestQuantitative Problem Solving with MeasurementHard
A manufacturer is designing a new cylindrical can with a radius of 3 cm and a height of 8 cm. What is the total surface area of the can, including the top and bottom? (Use π ≈ 3.14)
- A207.24 square cm
- B263.76 square cm
- C301.44 square cm
- D150.72 square cm
Show answer & explanationAnswer & explanation
Correct answer: A. 207.24 square cm
The total surface area of a cylinder is A = 2πr² + 2πrh. Given r = 3 cm, h = 8 cm, and π ≈ 3.14. A = 2 * 3.14 * (3²) + 2 * 3.14 * 3 * 8 = 2 * 3.14 * 9 + 2 * 3.14 * 24 = 56.52 + 150.72 = 207.24 square cm.
Why the other options are wrong
- B. Incorrect calculation, likely a mix-up of formula components.
- C. This is twice the lateral surface area, or an incorrect use of radius/height.
- D. This is only the lateral surface area (2πrh = 2 * 3.14 * 3 * 8 = 150.72).
Total Surface Area of a Cylinder
The sum of the areas of all surfaces of a cylinder, including the two circular bases and the curved lateral surface.
- Composed of two circular bases (2 * πr²) and one rectangular lateral surface (2πrh).
- Formula: A = 2πr² + 2πrh or A = 2πr(r + h).
- Units are square units.
Memory trick: Total surface area is like wrapping paper for the whole can.