GMAT Focus EditionQuantitative ReasoningMedium
A cylindrical tank has a radius of 4 meters and a height of 7 meters. If the tank is filled with water to 75% of its capacity, what volume of water is in the tank? (Use π ≈ 3.14)
- A351.68 cubic meters
- B197.82 cubic meters
- C263.76 cubic meters
- D210.00 cubic meters
Show answer & explanationAnswer & explanation
Correct answer: C. 263.76 cubic meters
The volume of a cylinder is given by the formula V = πr^2h, where 'r' is the radius and 'h' is the height. Given r = 4 meters and h = 7 meters, and π ≈ 3.14. Total volume of the tank = 3.14 * (4^2) * 7 = 3.14 * 16 * 7 = 3.14 * 112 = 351.68 cubic meters. The tank is filled to 75% of its capacity. So, the volume of water = 0.75 * 351.68 = 263.76 cubic meters.
Why the other options are wrong
- A. This is the total volume of the tank, not the volume of water at 75% capacity.
- B. Incorrect. This might be 75% of a miscalculated total volume or a different calculation error.
- D. Incorrect. This is a round number distractor, not based on the correct formula or percentage.
Geometric Formulas (Cylinder Volume)
The volume of a cylinder is calculated by multiplying the area of its circular base (πr²) by its height (h). This formula is fundamental for problems involving cylindrical containers or objects.
- Formula: V = πr²h.
- Units for volume are cubic units (e.g., m³, cm³).
- Ensure consistent units for radius and height.
- Often requires calculating a percentage of the total volume.
Memory trick: Pi R squared H, then percentage if it's not full, you see!