# Math Calculators

A cylinder tank volume calculator for determining the capacity of a horizontal cylinder tank. It uses the cylinder's length and radius as inputs and calculates the volume in cubic units.
Q: How can I calculate the volume of a horizontal cylinder tank?
A: To calculate the volume of a horizontal cylinder tank, you can use the following formulas:
- For the total volume of a horizontal cylindrical tank: V(tank) = πr²l, where r is the radius (equal to half the diameter) and l is the length of the tank.
- For the volume of a partially filled horizontal cylinder tank: V(fill) = V(tank) - V(segment), where V(segment) = (1/2)r²(θ - sinθ)l. The angle θ can be calculated as 2*arccos(m/r), where m is the fill height and r is the radius.

Q: How do I calculate the filled volume of a horizontal cylinder tank?
A: To calculate the filled volume of a horizontal cylinder tank, you need to determine whether the fill height (m) is less than or greater than half the diameter (d) of the tank.
- If the fill height (m) is less than 1/2 of the diameter (d), use the formula V(fill) = V(segment), where V(segment) = (1/2)r²(θ - sinθ)l.
- If the fill height (m) is greater than 1/2 of the diameter (d), use the formula V(fill) = V(tank) - V(segment), where V(tank) = πr²l is the total volume of the tank.

Q: What is the circular segment and how is it used in calculating the filled volume?
A: The circular segment is the shaded area in the cross-section of the tank. It represents the portion of the tank that is filled with liquid. The formula for the circular segment area is A = (1/2)r²(θ - sinθ), where r is the radius and θ is the central angle of the segment. By multiplying the circular segment area by the length of the tank, you can calculate the volume of the filled portion.

Q: How do I use the calculator for computing the volume of a partially filled horizontal cylinder tank?
A: To use the calculator, you need to input the tank diameter, tank length, and the reading on the dip stick, ruler, or measuring tape. The calculator will then provide a single detailed value for the volume of the partially filled tank.

Q: Are volume changes linear in a horizontal cylinder tank?
A: No, volume changes in a horizontal cylinder tank are not linear. The volume calculations involve complex formulas that take into account the shape and the filled height of the tank. The provided calculator simplifies the process by doing the calculations for you.