GED Mathematical Reasoning TestQuantitative Problem Solving with MeasurementHard
A gardener needs to cover a cylindrical planter with decorative paper. The planter has a radius of 0.5 feet and a height of 2 feet. What is the lateral surface area of the planter (the area of the side, not including the top and bottom)? (Use π ≈ 3.14)
- A6.28 square feet
- B3.14 square feet
- C1.57 square feet
- D9.42 square feet
Show answer & explanationAnswer & explanation
Correct answer: A. 6.28 square feet
The lateral surface area of a cylinder is found using the formula A = 2πrh. Given r = 0.5 feet, h = 2 feet, and π ≈ 3.14, the area is 2 * 3.14 * 0.5 * 2 = 6.28 square feet.
Why the other options are wrong
- B. This is the area of the top/bottom circle (πr² = 3.14 * 0.5² = 0.785) multiplied by 4, or 2πr (circumference).
- C. This is πr (3.14 * 0.5), which is half the circumference.
- D. This is the total surface area (2πr² + 2πrh) if r=0.5, h=2, and π=3.14, would be 2 * 3.14 * 0.25 + 6.28 = 1.57 + 6.28 = 7.85, so this is incorrect.
Lateral Surface Area of a Cylinder
The area of the curved side surface of a cylinder, excluding the top and bottom circular bases.
- Can be visualized as a rectangle when unrolled, with length = circumference and width = height.
- Formula: A = 2πrh.
- Units are square units.
Memory trick: Imagine unrolling the label from a can—that's the lateral surface.