Question

What is the best approximation of the volume of a sphere with a 6cm radius?

Answer 1

V= 904.8 cm rounded (904.78 cm^3) to the nearest tenth.

Explanation:

The volume of a sphere is given as 4 /3 π r^3

There is only one variable, the radius, which we are given in the problem.

since the radius is 6 cm, we can plug that in to the formula

4 /3 π 6 ^3

Put this into the calculator, and we see that the volume is

904.8 cm rounded (904.78 cm^3) to the nearest tenth.

Answer 2

Explanation:

An approximation uses rounded numbers just to get an answer. So pi would be called 3

V = 4/3 * pi * r^3

V = 4/3 * 3 * 6^3

V = 4 * 6^3

6^3 is about 200

V= 4 * 200

V = 800 cu cm.

Now you can get out your calculator and get a better answer.

V = 4/3 * pi * 6^3 = 1.333333 * 3.141592 * 216 = 904.7787

Why do an estimation? To tell you if your answer is in the right neighborhood. Considering what I did in the estimation, it's pretty close. It tells you that I have likely made "good enough" approximations and that 904 is likely right. Such skills are really necessary in every math class you take. 1000 things can go wrong in entering data. 904.7787 is likely as good an estimate as you will get. Pi goes out to thousands of places.