Comparing the Surface Area and Volume of a Sphere

A quick review: Answer the following questions. Click the blanks to reveal the answers.

A sphere is the set of all points that are ___________ equidistant from a given point, called the center.

To calculate the amount of material to cover a sphere the ___________ surface area formula is used.

The surface area of a sphere is measured in ______ square units.

The formula for surface area of a sphere is ________. S = 4πr².

To calculate the amount required to fill a sphere the formula for the ______ volume is used.

The volume of a sphere is measured in _____ cubic units.

The formula for volume of a sphere is _____. V = 4 3 πr³.

Below is a copy of the table obtained by entering in a graphing calculator the surface area formula, S = 4πr², in Y1 and the formula for volume, V = 4 3 πr³, in Y2. Note, "x" is sued for "r".

Radius	Surface Area	Volume
1	12.566	4.189
2	50.265	33.51
3	113.1	113.1
4	201.06	268.08
5	314.16	523.6
6	452.39	904.78
7	615.75	1436.8
8	804.25	2144.7
9	1017.9	3053.6
10	1256.6	4188.8
x	?	?

Find a sphere where the surface area and volume are equal.

The surface area and volume of a sphere are equal when a sphere has a radius of __ 3 units.
The constant in the formula for volume has a denominator of __. 3.
When there is a radius of __, 3, the constant 4 3 times 3 is equal to __. 4.
The constant 4 is the constant in the _______ surface area formula.

Observe the following computation for a sphere with radius of 3:

Conclusion: A sphere with a radius of 3 units has a _______ surface area that is _____ equal to its _____. volume.