GED Mathematical Reasoning TestQuantitative Problem Solving with MeasurementHard
A metal worker is fabricating a conical funnel with a radius of 6 cm and a slant height of 10 cm. If the worker needs to calculate the lateral surface area of the funnel (excluding the base) to determine the amount of material needed, what is the area, rounded to the nearest square centimeter? (Use π ≈ 3.14)
- A113 cm²
- B301 cm²
- C201 cm²
- D188 cm²
Show answer & explanationAnswer & explanation
Correct answer: D. 188 cm²
The lateral surface area of a cone is given by the formula A = πrl, where r is the radius and l is the slant height. Given r = 6 cm and l = 10 cm, A = 3.14 * 6 * 10 = 3.14 * 60 = 188.4 square centimeters. Rounded to the nearest square centimeter, this is 188 cm².
Why the other options are wrong
- A. This would be the area of the base (πr²) or a calculation error.
- B. This would be an overestimation or calculation error.
- C. This might be the result if total surface area (including base) was calculated, or a different formula was used.
Lateral Surface Area of a Cone
The lateral surface area of a cone is the area of its curved side, excluding the base, calculated using its radius and slant height.
- Formula: A = πrl, where r is radius and l is slant height.
- Slant height (l) is the distance from the apex to a point on the circumference of the base.
- Measured in square units.
Memory trick: Pi R L, for the cone's side spell!