Height of Oblique Cylinder given Total Surface Area Calculator

Formula Used:

\[ h = \frac{TSA - (2 \pi r^2)}{2 \pi r} \times \sin(\angle Slope) \]

Total Surface Area of Oblique Cylinder (TSA):

m²

Radius of Oblique Cylinder (r):

Angle of Slope of Oblique Cylinder (∠Slope):

rad

Height of Oblique Cylinder (h):

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1. What is the Height of Oblique Cylinder given Total Surface Area Formula?

The formula calculates the height of an oblique cylinder using its total surface area, radius, and the angle of slope. It provides a mathematical relationship between these geometric properties of an oblique cylinder.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \frac{TSA - (2 \pi r^2)}{2 \pi r} \times \sin(\angle Slope) \]

Where:

\( h \) — Height of Oblique Cylinder (m)
\( TSA \) — Total Surface Area of Oblique Cylinder (m²)
\( r \) — Radius of Oblique Cylinder (m)
\( \angle Slope \) — Angle of Slope of Oblique Cylinder (rad)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \sin \) — Sine trigonometric function

Explanation: The formula derives the height by first calculating the lateral surface area from the total surface area, then using the sine function to account for the oblique angle.

3. Importance of Height Calculation

Details: Calculating the height of an oblique cylinder is essential for various engineering and architectural applications, including structural design, volume calculations, and spatial planning where non-vertical cylindrical elements are involved.

4. Using the Calculator

Tips: Enter total surface area in square meters, radius in meters, and angle of slope in radians. All values must be positive (surface area > 0, radius > 0, angle ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is an oblique cylinder?
A: An oblique cylinder is a cylinder where the sides are not perpendicular to the bases. The axis is inclined at an angle to the base.

Q2: Why is the sine function used in this formula?
A: The sine function accounts for the inclination angle of the oblique cylinder, relating the true height to the slanted lateral surface.

Q3: What are typical units for these measurements?
A: Surface area is typically in square meters (m²), radius and height in meters (m), and angle in radians (rad) or degrees (converted to radians for calculation).

Q4: Can this formula be used for right cylinders?
A: Yes, for right cylinders the angle of slope is 90 degrees (π/2 radians), making sin(∠Slope) = 1, simplifying the formula.

Q5: What if I have the angle in degrees instead of radians?
A: Convert degrees to radians by multiplying by π/180 before entering the value in the calculator.