Base Radius Of Cone Given Lateral Surface Area And Slant Height Calculator

Formula Used:

\[ Base\ Radius\ of\ Cone = \frac{Lateral\ Surface\ Area\ of\ Cone}{\pi \times Slant\ Height\ of\ Cone} \] \[ r_{Base} = \frac{LSA}{\pi \times h_{Slant}} \]

Base Radius of Cone (rBase):

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1. What is the Base Radius of Cone?

The Base Radius of a Cone is defined as the distance between the center and any point on the circumference of the base circular surface of the Cone. It is a fundamental geometric parameter used in various cone calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Base\ Radius\ of\ Cone = \frac{Lateral\ Surface\ Area\ of\ Cone}{\pi \times Slant\ Height\ of\ Cone} \] \[ r_{Base} = \frac{LSA}{\pi \times h_{Slant}} \]

Where:

\( LSA \) — Lateral Surface Area of Cone (m²)
\( h_{Slant} \) — Slant Height of Cone (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula derives from the relationship between the lateral surface area, slant height, and base radius of a cone.

3. Importance of Base Radius Calculation

Details: Calculating the base radius is essential for determining other cone properties such as volume, total surface area, and for various engineering and architectural applications involving conical structures.

4. Using the Calculator

Tips: Enter lateral surface area in square meters (m²) and slant height in meters (m). Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between slant height and height of a cone?
A: Slant height is the distance from the apex to any point on the circumference of the base along the lateral surface, while height is the perpendicular distance from the apex to the base center.

Q2: Can this formula be used for truncated cones?
A: No, this formula is specifically for right circular cones. Truncated cones have different formulas for lateral surface area calculations.

Q3: What are the units for base radius?
A: The base radius is typically measured in meters (m), but can be in any length unit as long as it's consistent with the input units.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on the input values. The accuracy depends on the precision of the input measurements.

Q5: What if I have the total surface area instead of lateral surface area?
A: You would need to subtract the base area from the total surface area first to get the lateral surface area before using this formula.