ACT (Enhanced)MathematicsHard
A civil engineer is calculating the volume of concrete needed for a cylindrical support column. The column has a radius of 0.5 meters and a height of 6 meters. What is the volume of the concrete needed, in cubic meters?
- A6π m³
- B3π m³
- C12π m³
- D1.5π m³
Show answer & explanationAnswer & explanation
Correct answer: D. 1.5π m³
The formula for the volume of a cylinder is V = πr²h. Given r = 0.5 meters and h = 6 meters, substitute these values into the formula: V = π * (0.5)² * 6 = π * 0.25 * 6 = 1.5π cubic meters.
Why the other options are wrong
- A. This would be if the radius was the height, or if radius was 1 and height was 6.
- B. This would be if the radius was 1 meter.
- C. Incorrect calculation, possibly using diameter instead of radius or squaring the wrong term.
Volume of a Cylinder
The volume of a cylinder is the product of the area of its circular base and its height. V = πr²h.
- r is the radius of the circular base.
- h is the height of the cylinder.
- Units are cubic (e.g., m³).
Memory trick: Pi-R-Squared-H: 'P'ut 'R'adius 'S'quared and 'H'eight in the formula.