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The formula calculates the diameter of a hemisphere when its total surface area is known. It is derived from the total surface area formula of a hemisphere and provides an efficient way to determine the diameter without direct measurement.
The calculator uses the formula:
Where:
Explanation: The formula rearranges the total surface area equation to solve for diameter, using the mathematical constant π and square root function.
Details: Calculating the diameter from surface area is essential in various engineering, architectural, and manufacturing applications where hemispherical shapes are used, and direct measurement of diameter is not feasible.
Tips: Enter the total surface area in square meters. The value must be positive and valid. The calculator will compute the corresponding diameter.
Q1: What is the relationship between diameter and surface area in a hemisphere?
A: The diameter is directly related to the square root of the surface area, as shown in the formula \( D = 2 \times \sqrt{\frac{TSA}{3\pi}} \).
Q2: Can this formula be used for spheres as well?
A: No, this specific formula is for hemispheres. For spheres, the formula would be different as the surface area calculation differs.
Q3: What are the units used in this calculation?
A: The calculator uses meters for diameter and square meters for surface area, but the formula works with any consistent unit system.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values and using the exact value of π in computations.
Q5: What if I have the curved surface area instead of total surface area?
A: The formula would need to be adjusted since total surface area includes both the curved surface and the base area of the hemisphere.