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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.[1]
Steps
Help Finding Volume of a Cone
Calculating the Volume of a Cone
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1Find 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.[2] If you know the circumference, divide it by 2π to get the diameter.[3] 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).
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2Use 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.[4]Advertisement
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3Find 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.[5] 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.
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4Multiply 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.[6] 3
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5Divide 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.[7]
Community Q&A
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QuestionWhat if the given is slant height and base? How to find the volume of cone?
Community AnswerUse the Pythagorean Theorem to find the height, using the slant length as the hypotenuse and half the base as one side. -
QuestionHow do I calculate the radius of a cone when I already have the volume?Community AnswerYou 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.
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QuestionIf I double the height, will I double the volume?
DonaganTop AnswererYes.
References
- ↑ https://www.omnicalculator.com/math/cone-volume
- ↑ https://sciencing.com/radius-diameter-7254718.html
- ↑ https://sciencing.com/calculate-radius-circumference-7804860.html
- ↑ https://www.mathwarehouse.com/geometry/circle/area-of-circle.php
- ↑ https://www.cuemath.com/measurement/volume-of-cone/
- ↑ https://www.omnicalculator.com/math/cone-volume
- ↑ https://www.cuemath.com/measurement/volume-of-cone/
About This Article
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. For helpful sheets you can print out and take with you, read on!
