GMAT Focus EditionQuantitative ReasoningMedium
A cylindrical tank has a radius of 5 meters and a height of 10 meters. If the tank is filled with water at a rate of 25π cubic meters per hour, how many hours will it take to fill the tank completely?
- A10 hours
- B15 hours
- C20 hours
- D5 hours
Show answer & explanationAnswer & explanation
Correct answer: A. 10 hours
The volume of a cylinder is given by V = πr²h. Given r = 5m and h = 10m, the volume V = π(5)²(10) = π(25)(10) = 250π cubic meters. The filling rate is 25π cubic meters per hour. Time to fill = Total Volume / Filling Rate = 250π / 25π = 10 hours.
Why the other options are wrong
- B. This is incorrect; it might be a result of miscalculating the volume or division.
- C. This is incorrect; it might be a result of miscalculating the volume or division.
- D. This is incorrect; it might be a result of miscalculating the volume or division.
Geometric Formulas (Cylinder Volume)
Calculating the amount of space occupied by a three-dimensional cylindrical object.
- Formula for cylinder volume: V = πr²h, where r is radius and h is height.
- Units of volume are cubic units (e.g., m³).
- Often combined with rate problems to find time to fill/empty.
Memory trick: Volume is pie-R-squared-H, then time is volume over flow rate.