ACT (Enhanced)MathematicsMedium
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 8 meters. If concrete costs $75 per cubic meter, what is the total cost of the concrete for one column? (Use π ≈ 3.14)
- A$942.00
- B$235.50
- C$376.80
- D$471.00
Show answer & explanationAnswer & explanation
Correct answer: D. $471.00
First, calculate the volume of the cylinder using V = πr^2h. Then, multiply the volume by the cost per cubic meter to find the total cost.
Why the other options are wrong
- A. This results from squaring the diameter instead of the radius, or doubling the correct cost.
- B. This is the result of using diameter instead of radius, or a calculation error.
- C. This results from an incorrect calculation of the volume or cost.
Volume of a Cylinder
The amount of three-dimensional space occupied by a cylinder, calculated by multiplying the area of its base by its height.
- Formula: V = πr^2h, where r is the radius and h is the height.
- The base is a circle, with area πr^2.
- Units for volume are cubic units (e.g., m^3, ft^3).
Memory trick: Pi r squared h, then multiply by cost, no math crash!