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How to Calculate the Volume of a Cone

Steps

Help Finding Volume of a Cone

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 .5 inches (1.3 cm).
  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 getA = π(.5)2and 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 1.5 inches (1.3 cm). 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.2x 1.5 in = 1.19 in.3
  5. Divide the product by three.Simply divide 1.19 in.3by 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.

Community Q&A

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  • Question
    What if the given is slant height and base? How to find the volume of cone?
    wikiHow Contributor
    Community Answer
    Use the Pythagorean Theorem to find the height, using the slant length as the hypotenuse and half the base as one side.
    Thanks!
  • Question
    How do I calculate the radius of a cone when I already have the volume?
    wikiHow Contributor
    Community Answer
    You would do: V = 1/3 *π*r^2. Divide volume by 3. Divide volume by π, then square root that number. And there is your radius.
    Thanks!
  • Question
    If I double the height, will I double the volume?
    Top Answerer
    Thanks!
  • Question
    How do I find the volume of a cone if the diameter is given, not the radius?
    wikiHow Contributor
    Community Answer
    Since the volume of a cone is pi times the radius squared times the height divided by 3, if you know the diameter, you simply divide by two to find the radius, which you then plug into the formula.
    Thanks!
  • Question
    How do I work out the perpendicular height of a cone without any radii or volume measures?
    Top Answerer
    You can't do it.
    Thanks!
  • Question
    How do I calculate the radius of a base of a cone?
    Top Answerer
    You must be given either the diameter of the base, the area of the base, the circumference of the base, or the volume of the cone. Then work backwards to the radius from the formula for the volume, base area or base circumference of a cone.
    Thanks!
  • Question
    Where did the 1/3 in the formula come from?
    wikiHow Contributor
    Community Answer
    The volume of a cone is one-third the volume of a cylinder of the same height and radius.
    Thanks!
  • Question
    How do I get the total surface area of a cone?
    Top Answerer
    For a right cone, the lateral surface area is πrl, where r is the radius and l is the slant height. If you want to include the base area, add πr².
    Thanks!
  • Question
    If the quadrant of a circle of radius 14 cm is folded to a cone, how can I find the radius of this cone?
    Top Answerer
    Double the radius, and multiply that by pi: that's the circumference of the circle. Divide by 4: that's the arc of the quadrant and the circumference of the cone. Divide by twice pi: that's the radius of the cone.
    Thanks!
  • Question
    Given the height and radius of a cone are 3 cm and 4 cm respectively, calculate the total surface area of the cone.
    Top Answerer
    With the Pythagorean theorem, use the radius and the height to calculate the slant height of the cone, then multiply the slant height by the radius by pi. That gives you the lateral area of the cone. To that you add the base area of the cone, which is found by multiplying pi by the square of the radius. The total surface area is found by adding the lateral surface area to the base area.
    Thanks!
Unanswered Questions
  • What is the formula for the surface area of a FULL cone (not half a cone)?
  • How do I find the area of the base of a cone?
  • How do I figure out the volume of a cone?
  • How do I find height and radius of a con with only volume?
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Video

Quick Summary

To calculate the volume of a cone, start by finding the cone's radius, which is equal to half of its diameter. Next, plug the radius into the formula A = πr^2, where A is the area and r is the radius. Once you have the area, multiply it by the height of the cone. Finally, divide that number by 3 to find the volume of the cone. Remember to write your answer in cubic units.

Did this summary help you?
  • 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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Date: 04.12.2018, 06:39 / Views: 41375