finding-the-radius-of-a-sphere-given-the-volume

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Interactive video lesson plan for: Finding the radius of a sphere given the volume

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The video reviews how to find the radius of a sphere given the volume.
The question that is solved is,
Find the radius of a sphere with a volume of 72 meters squared.
The volume formula is 4/3 pi r cubed.
In order to solve for the radius you have to undo the formula.
Transcript
The radius of a sphere with a volume of 72 m^2
This is a backwards problem. There is no easy way to do it other than just to undo it. Let’s see what we have. We have the volume and we know that volume formula is equal to 4/3 pi radius cubed. We know the volume is 72 so I'm just going to plug in 72. Now the only variable we have in this formula is the radius, but we have to get it by itself by undoing all this stuff. To undo a fraction we multiply by its reciprocal so we are going to flip it upside down and multiply both sides by 3/4 and that cancels out the 4/3 so we will multiply 72 by 3/4 so let’s multiply 3 times 72 and divide that by 4 so the left side will simplify to 54 so we have 54 = pi radius cubed. We are getting closer. Now we need to get rid of pi which is 3.14 so we can just divide by that. We will take 54 and divide both sides by pi so 54 divided by pi and I get 17.9 is equal to radius cubed. Now how do you undo a cube? You take a cube root. What we will do is take the cube root of 17.9 I will show you what to do. Go to the Math button and under Math pick the 4th choice which is the cube root. You can choose it or go down to 4. Enter 17.9 and I will type in instead of pulling down my answer. I get 2.58, so our radius is 2.58 in meters. That is how you find the radius of a sphere from the volume. A little bit of undoing and algebra that you will manipulate.

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Tagged under: sphere,radius,radius volume,Volume (Dimension),Mathematics (Field Of Study),moomoomath

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