Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryHard
A packaging engineer is designing a container in the shape of a cylinder. The cylinder has a radius of 4 cm and a height of 10 cm. What is the approximate surface area of the cylinder, including the top and bottom circular bases?
- A201.06 cm²
- B402.12 cm²
- C125.66 cm²
- D351.86 cm²
Show answer & explanationAnswer & explanation
Correct answer: D. 351.86 cm²
The surface area of a cylinder is given by the formula SA = 2πrh + 2πr², where r is the radius and h is the height. Given r = 4 cm and h = 10 cm. Area of two bases = 2 * π * (4)² = 2 * π * 16 = 32π. Area of lateral surface = 2 * π * 4 * 10 = 80π. Total surface area = 32π + 80π = 112π. Using π ≈ 3.14159, SA ≈ 112 * 3.14159 ≈ 351.858 cm², which is approximately 351.86 cm².
Why the other options are wrong
- A. This is approximately 64π, possibly from using 2πr² only for the bases, or 2πr * h/2.
- B. This is approximately 128π, possibly from 2πr(r+2h) or other miscalculation.
- C. This is approximately 40π, possibly from using 2πrh/2.
Surface Area of a Cylinder
The total area of the outer surface of a cylinder, including its two circular bases and its lateral (curved) surface.
- Formula: SA = 2πrh + 2πr².
- 2πr² accounts for the area of the two circular bases.
- 2πrh accounts for the area of the lateral (curved) surface.
Memory trick: Two 'Circles' for top/bottom, one 'Rectangle' for the curved side.