ACT (Enhanced)MathematicsMedium
A civil engineer is calculating the volume of concrete needed for a cylindrical pillar. The pillar has a radius of 0.5 meters and a height of 4 meters. Using π ≈ 3.14, what is the volume of the concrete pillar in cubic meters?
- A6.28 m³
- B3.14 m³
- C12.56 m³
- D9.42 m³
Show answer & explanationAnswer & explanation
Correct answer: B. 3.14 m³
The volume of a cylinder is given by the formula V = πr²h. Given r = 0.5 m and h = 4 m, and using π ≈ 3.14: V = 3.14 * (0.5)² * 4 = 3.14 * 0.25 * 4 = 3.14 * 1 = 3.14 m³.
Why the other options are wrong
- A. This would be 2 * π * r * h (lateral surface area) or if radius was 1.
- C. This would be if the radius was 1 meter (π * 1^2 * 4 = 4π ≈ 12.56).
- D. This is a plausible distractor, perhaps from a calculation error.
Volume of a Cylinder
The volume of a cylinder is the amount of space it occupies, calculated by multiplying the area of its circular base by its height.
- Formula: V = πr²h, where r is the radius and h is the height.
- Units are cubic (e.g., m³, cm³).
- π (pi) is a mathematical constant, approximately 3.14159.
Memory trick: Volume is Pi-R-squared for the base, times H for height.