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Radius of Cone Calculator Online

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The Radius of Cone Calculator is designed to determine the base radius of a cone when certain measurements are known. It is particularly handy for quick calculations in mathematical and engineering problems, helping professionals and students alike to save time and ensure accuracy.

Formula of Radius of Cone Calculator

Formula Using Volume

To find the radius of a cone’s base using its volume, the following formula is use:

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r = sqrt(3V / (pi * h)) Where:

  • r is the radius of the cone’s base.
  • V is the volume of the cone.
  • h is the height of the cone.
  • pi is a constant approximately equal to 3.14159.

Formula Using Surface Area

To calculate the radius using the surface area of the cone, the formula is:

r = A / (pi * l) Where:

  • r is the radius of the cone’s base.
  • A is the surface area of the cone.
  • l is the slant height of the cone.
  • pi is again approximately 3.14159.

Conversion Table for Common Measurements

MeasurementValue (in cm)Notes
Small cone height10 cmTypical height for a small cone
Small cone volume314 cm³Volume with radius = 5 cm
Large cone height50 cmTypical height for a large cone
Large cone volume3925 cm³Volume with radius = 14 cm

Example of Radius of Cone Calculator

Scenario:

Calculate the radius of a cone with a volume of 314 cm³ and a height of 10 cm.

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Calculation:

  1. Use the formula: r = sqrt(3V / (pi * h))
  2. Substitute the values: r = sqrt(3 * 314 / (3.14159 * 10))
  3. Simplify the expression: r = sqrt(942 / 31.4159) = sqrt(29.979)
  4. Result: r = 5.477 cm

This calculation shows the radius of the cone’s base is approximately 5.477 cm.

Most Common FAQs

What is the most accurate way to measure the volume of a cone?

To accurately measure the volume of a cone, you need the radius of the base and the height of the cone. The volume is then calculated using the formula V = (1/3) * pi * r^2 * h.

Can this calculator be use for truncated cones?

Yes, the Radius of Cone Calculator can also be adapt to calculate the dimensions of a truncated cone, though the formulas will vary slightly due to the different geometric setup.

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