The ASVAB Tutor Presents Answer to ASVAB Math Question on Volume of a Sphere

Mathematics Knowledge

Yesterday I presented a question about volume?  Do you know how to find the volume of a sphere?  The question was: If the radius of a sphere is 1, what is its volume?

In working as an ASVAB tutor, I place a strong emphasis on the significance of knowing the formulas for the geometry questions on the ASVAB.  Area, circumference, volume, and surface area are among the formulas I remind my students they need to know.  The volume of a sphere is one of the more challenging formulas.

Volume of a sphere

V = 4/3pr³

Some people find it difficult to multiply 4/3 by p.  It is time consuming to say the least.

I tell my students to remember an easier version of this formula.

When 4/3 is multiplied by p, the answer is 4.1762.

I encourage my students to learn the formula for sphere to be this:

V = 4.1762r³

If the answer choices are far apart in value, I tell my students to use an even easier formula.

V = 4r³

This simpler version is just an estimate.  The real answer will be a bit bigger, but when working with a multiple choice test it is probably enough to find the correct answer.

The correct answer for the volume of a sphere when the radius is 1 is

V = 4.1762(1)³ = 4.1762(1) = 4.1762

The estimate is

V = 4(1)³ = 4(1) = 4.

You can see that the estimate is close enough to the real answer to succeed in picking the correct answer in this multiple-choice.