1. What is Top Radius of Frustum of Cone given Top Area?

The top radius of a frustum of a cone is the radius of the smaller circular base when the top area is known. This calculation is essential in geometry and various engineering applications involving conical structures.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_{top} \) — Top radius of the frustum (m)
• \( A_{top} \) — Top area of the frustum (m²)
• \( \pi \) — Mathematical constant approximately equal to 3.14159

Explanation: The formula derives from the basic area of a circle formula, rearranged to solve for the radius when the area is known.

3. Importance of Top Radius Calculation

Details: Calculating the top radius is crucial for determining the dimensions of conical structures, volume calculations, surface area computations, and various engineering applications involving frustums of cones.

4. Using the Calculator

Tips: Enter the top area in square meters. The value must be positive and greater than zero. The calculator will compute the corresponding top radius.

5. Frequently Asked Questions (FAQ)

Q1: What is a frustum of a cone?
A: A frustum of a cone is the portion of a cone that remains after cutting off the top by a plane parallel to the base.

Q2: Can this formula be used for any circular area?
A: Yes, this formula applies to any circular area to find the corresponding radius, not just frustums of cones.

Q3: What units should I use for the calculation?
A: Use consistent units - typically square meters for area and meters for radius. The calculator assumes metric units.

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: Can I calculate the bottom radius using a similar formula?
A: Yes, the same formula applies to calculate the bottom radius if you know the bottom area: \( r_{bottom} = \sqrt{\frac{A_{bottom}}{\pi}} \)