FAA Aviation Mechanic General (AMG)Physics, Math and Fluid LinesEasy
A technician needs to determine the height of a cylindrical reservoir with a known volume of 157 cubic inches and a radius of 2 inches. Using the formula V = πr²h, what is the height of the reservoir?
- A3.14 in
- B6.25 in
- C25 in
- D12.5 in
Show answer & explanationAnswer & explanation
Correct answer: D. 12.5 in
Rearranging the formula: h = V ÷ (πr²) = 157 ÷ (3.1416 × 4) = 157 ÷ 12.566 = 12.5 in.
Why the other options are wrong
- A. This mistakenly uses π alone instead of the full denominator.
- B. This is half the correct value, likely from a doubling error.
- C. This is double the correct value.
Cylinder Volume Formula
The volume of a cylinder equals π times the radius squared times the height (V = πr²h), and can be rearranged to solve for any unknown variable.
- V = πr²h
- Solve for h: h = V ÷ (πr²)
- Solve for r: r = √(V ÷ (πh))
Memory trick: Volume equals pi times radius squared times height — rearrange to isolate the mystery.