Question

The surface area of this cylinder is 1,582.56 square feet. What is the height?

Answer 1

What's the height of a cylinder formula?

There are five basic equations which completely describe the cylinder with given radius r and height h:

1. Volume of a cylinder: V = π * r² * h,
2. Base surface area of a cylinder: A_b = 2 * π * r²,
3. Lateral surface area of a cylinder: A_l = 2 * π * r * h,
4. Total surface area of a cylinder: A = A_b + A_l,
5. Longest diagonal of a cylinder: d² = 4 * r² + h².

Sometimes, however, we have a different set of parameters. With this height of a cylinder calculator you can now quickly use ten various height of a cylinder formulas which can be derived directly from the above equations:

1. Given radius and volume: h = V / (π * r²),
2. Given radius and lateral area: h = A_l / (2 * π * r),
3. Given radius and total area: h = (A - 2 * π * r²) / (2 * π * r),
4. Given radius and longest diagonal: h = √(d² - 4 * r²),
5. Given volume and base area: h = 2 * V / A_b,
6. Given volume and lateral area: h = A_l² / (4 * π * V),
7. Given base area and lateral area: h = √(A_l² / (2 * π * A_b)),
8. Given base area and total area: h = (A - A_b) / √(2 * A_b * π),
9. Given base area and diagonal: h = √(d² - 2 * A_b / π),
10. Given lateral area and total area: h = A_l / √(2 * π * (A - A_l)).