How do I Find the Radius of a Base Circle When Given the Volume & Height?
Finding the radius of the base circle of a cone can tell you exactly how much ice cream you can stuff into your ice cream cone. It can also tell you whose head will fit in the party hats or how much floor space you might have in the backyard tepee. It is not overly difficult to find the radius of a base circle, and when given the numerical value of the volume and the height of the cone, it becomes a matter of applying basic math.
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Instructions
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Rearrange the standard formula for finding cone volume. Because the radius and height are the easiest to physically measure, standard algebraic formulas are given for volume, surface area or the slant height of the cone, which assume the values of radius (r) and height (h) are known. The standard formula for volume (V) is: V= (1/3)πr^2h. These formulas can generally be rearranged to give numerous different values for the cone.
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Get "r" on its own when rearranging the formula so that it now reads: r = √[(3xV) / (π x h)]. By taking the "r" to one side, you have to reverse the square of "r," which is why it is now a square root formula; what you do to one side you must do to the other. Similarly when you moved "V" across the equation, you change the divide to times. If you assume V = 5 and h = 3, you can now input these known values into the formula. So, r = √[(3x5) / (π x 3)].
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Complete the equations within the brackets so that it reads: r = √[(15) / (3.14 x 3)]. One more step and the formula reads: r = √[15 / 9.42]. So r = √1.5923. The square root of 1.5923 is 1.2618, which is the radius of your base circle. You can use the rearranged formula and then input your own values for "V" and "h" to find the radius of your own cone's base circle.
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References
- Photo Credit inside of a cone image by timur1970 from Fotolia.com
