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# volume of a pyramid

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The volume of this cone is 201,456.12 cubic millimeters. What is the radius of this cone?

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

Apr 29, 2021

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To find the radius of a cone, you need not one, but two criteria to derive it. Because all that is given is the volume, it is not possible to find the radius of this cone unless given the height, too. This is because to determine a variable such as the radius, we must have all other criteria for the formula to find the volume to figure it out. Because the formula for the volume of a cone is 1/3 * pi * r^2 * h, we need the height to find out the radius.

So it is not possible.

But, if you were to have said a sphere, we would be able to figure it out because the volume of a sphere is 4/3 * pi * r^3 so there are no other criteria except for the radius needed to figure out the volume.

Now, I noticed that the question title actually says "volume of a pyramid", so maybe there was a typo. Still, this would be impossible due to the fact that the volume of a pyramid formula states, $${\displaystyle V={\frac {1}{3}}lwh},$$ where is the slant height, is the width, and is the height.

Apr 29, 2021
edited by NotGuest  Apr 29, 2021