Question: Volume of Sphere

Comment on Volume of Sphere

Why can't we use volume of sphere formula: Volume = (4/3)(pi)r^3
greenlight-admin's picture

That's totally acceptable, except most people don't know that formula, and the formula is not required knowledge for the GRE.

So, the solution provided in the video shows that we can solve the question by applying logic rather than by using a formula.

Is sphere included for gre exam?
greenlight-admin's picture

As I mention at the beginning of the video, you do not need to know the formula for the volume of a sphere. However, you should know what a sphere is, since it's possible that there could be a question involving a sphere.

wooow. mathematical magic

Clever approach. I think I'll remember it as "thinking inside the box".
greenlight-admin's picture

Ha!!! I love it!

Last thing. After seeing your presentation here, I wondered how big the difference is between the volume of a sphere and a cube that just contains it. Based on my calculations, a sphere is approximately half the volume of the cube (5% more than half). (I plugged in 1/2 Diameter in for radius in formula for volume of sphere).

Volume of sphere = 1/2 • volume of cube • 1.05
V = 1/2 • diameter^3 • 1.05
Volume of sphere = .53 • volume of cube
V = .53D^3

I don't know if anyone else would find this particularly useful, but I thought it was interesting.
greenlight-admin's picture

Interesting indeed. It certainly LOOKS like such a sphere would fill up way more than half of the cube. My calculations say that a sphere takes up 52.3% of the cube's volume.

I had one more question about a sphere. Given we can find the volume of a cylinder by finding the area of a circle and multiplying it by the height of a circle, could we do something similar for a sphere? I took the area half a circle and then multiplied it by the circumference of the circle in radians, thinking that the circumference might be analagous to the height for a cylinder, but the resulting volume wasn't correct. (I got 36 vs correct answer of 32, given a radius of 2). It doesn't matter for the test, but I was curious and figured you might know.

Regarding my previous comment on spheres, you are right it is 52.3. Since then I've thought that (π/6)D^3 is a good way to remember volume of a sphere, because you can see in the expression that the volume of a sphere approximately half of the volume of a corresponding cube, and it keeps the π in the calculations.
greenlight-admin's picture

That would seem like a good way to calculate the volume of a sphere. The problem with that approach is that, if we slice a sphere into tiny circles, the size of the circles vary.

On the other hand, if we slice a CYLINDER into tiny circles, the size of the circles are always the same.


Will NEVER be on the GRE. We don't need to know volume of a sphere at all, and this has never appeared on the GRE whatsoever. Secondly, the logical leaps required here are out of scope.
greenlight-admin's picture

I agree that you don't need to know the volume of a sphere. In fact, that's the very first thing I say and my solution.
The one logical step required solve this question is well within the scope of the GRE, especially when you consider the fact that Quantity B is three times the value of Quantity A.

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