GED Mathematical Reasoning TestQuantitative Problem Solving with MeasurementHard
A manufacturer is designing a new spherical display case with a radius of 3 feet. To calculate the amount of glass needed, they must find the total surface area of the sphere. What is the total surface area of the display case, rounded to the nearest square foot? (Use π ≈ 3.14)
- A57 square feet
- B28 square feet
- C113 square feet
- D151 square feet
Show answer & explanationAnswer & explanation
Correct answer: C. 113 square feet
The surface area of a sphere is given by the formula A = 4πr². Given a radius (r) of 3 feet, A = 4 * 3.14 * (3)² = 4 * 3.14 * 9 = 12.56 * 9 = 113.04 square feet. Rounded to the nearest square foot, this is 113 square feet.
Why the other options are wrong
- A. This would be the result if 2πr² was used, or a calculation error.
- B. This would be the result if the formula for the area of a circle (πr²) was used, or a calculation error.
- D. This would be the result if the volume formula (4/3πr³) was used, or a significant overestimation.
Surface Area of a Sphere
The surface area of a sphere is the total area of its outer surface, calculated by 4 times pi (π) times the square of its radius.
- Formula: A = 4πr²
- Measured in square units.
- Represents the 2D surface of a 3D object.
Memory trick: Four Pi R Squared, for the sphere's full area declared!