Calculate the Volume of a Cone

You can calculate the volume of a cone easily once you know its height and radius and can plug those measurements into the formula for finding the volume of a cone. The formula for finding the volume of a cone is v = hπr2/3.

Steps

Help Finding Volume of a Cone

Doc:Volume of a Cone Diagram,Volume of a Cone Calculator

Calculating the Volume of a Cone

  1. Find the radius. If you already know the radius, then you can move on to the next step. If you know the diameter, divide it by 2 to get the radius. If you know the circumference, divide it by 2π to get the diameter. And if you don't know any of the measurements of the shape, just use a ruler to measure the widest pie circular base (the diameter) and divide that number by 2 to get the radius. Let's say the radius of this cone's circular base is {{safesubst:#invoke:convert|convert}}.
  2. Use the radius to find the area of the base circle. To find the area of the base circle, you can just use the same formula you'd use to find the area of a circle: A = πr2. Plug ".5" in for r to get A = π(.5)2 and square the radius and multiply it by the value of π to find the area of the circular base. π(.5)2 = .79 in.2.
  3. Find the height of the cone. If you know it already, write it down. If you don't know it, use a ruler to measure it. Let's say the height of the cone is 1{{safesubst:#invoke:convert|convert}}. Make sure that the height of the cone is written in the same measurements as the radius.
  4. Multiply the area of the base by the height of the cone. Multiply the area of the base, .79 in.2, by the height, 1.5 in. So, .79 in.2 x 1.5 in = 1.19 in.3
  5. Divide the product by three. Simply divide 1.19 in.3 by 3 to find the volume of a cone. 1.19 in.3/3 = .40 in.3. Always state the volume in cubic units because it's a measure of three-dimensional space.



Tips

  • Make sure you have accurate measurements.
  • Don't do this while there's still ice cream in the cone.
  • Make sure the measurements are all in the same type/unit of measurement.
  • How it Works:
    • In this method, you are basically calculating the volume of the cone as if it was a cylinder. When you calculate the area of the base circle, and multiply it by the height, you are "stacking" the area up until it reaches the height, thus creating a cylinder. And because a cylinder can fit three cones of its matching measurements, you multiply it by one third so that it's the volume of a cone. This provides you with the volume of the cone.
  • The radius, the height, and the slant height ---slant height is measured down the sloping side of the cone, while the true height is measured through the middle from the tip to the center of the circular base --- form a right triangle. Therefore, they are related by the Pythagorean Theorem: (radius)2+ (height)2 = (slant height)2

Warnings

  • Make sure to divide by 3

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