Digital SATMath: Geometry and TrigonometryMedium
A cylindrical water tank has a diameter of 8 feet and a height of 10 feet. If 1 cubic foot of water is approximately 7.48 gallons, what is the maximum volume of water, in gallons, the tank can hold?
- A502.65 gallons
- B75167.36 gallons
- C37583.68 gallons
- D1884.96 gallons
Show answer & explanationAnswer & explanation
Correct answer: C. 37583.68 gallons
First, calculate the volume of the cylinder. The radius is half the diameter, so r = 8/2 = 4 feet. Volume (V) = πr²h = π * (4 feet)² * 10 feet = π * 16 * 10 = 160π cubic feet. Now, convert to gallons: 160π cubic feet * 7.48 gallons/cubic foot ≈ 160 * 3.14159 * 7.48 ≈ 37583.68 gallons.
Why the other options are wrong
- A. This would be the volume in cubic feet if the radius was half of the diameter, but not converted to gallons.
- B. This is double the correct answer, perhaps from using the diameter instead of radius squared in the volume formula.
- D. This is the volume in cubic feet (160π), not converted to gallons.
Volume of a Cylinder
The amount of space occupied by a three-dimensional cylindrical object.
- Formula: V = πr²h (where r is radius, h is height)
- Units are cubic (e.g., cubic feet, cubic meters).
- Represents the capacity of the cylinder.
Memory trick: Volume is like filling a box: Area of the base times the height.