CK-12 Geometry Concepts

11.7. Spheres http://www.ck12.org

Surface areais a two-dimensional measurement that is the total area of all surfaces that bound a solid.Volumeis a
three-dimensional measurement that is a measure of how much three-dimensional space a solid occupies.

Guided Practice

1. Find the surface area of the figure below.


2. The surface area of a sphere is 100πin^2. What is the radius?


3. A sphere has a volume of 14137. 167 f t^3 , what is the radius?

Answers:

1. This is a hemisphere. Be careful when finding the surface area of a hemisphere because you need to include the
   area of the base. If the question asked for the lateral surface areanotinclude the bottom.

SA=πr^2 +

1

2

4 πr^2

=π( 62 )+ 2 π( 62 )

= 36 π+ 72 π= 108 πcm^2

2. Plug in what you know to the formula and solve forr.

100 π= 4 πr^2

25 =r^2

5 =r

3. Because we have a decimal, our radius might be an approximation. Plug in what you know to the formula and
   solve forr.

14137. 167 =

4

3

πr^3

3

4 π

· 14137. 167 =r^3

3375 =r^3

At this point, you will need to take thecubed rootof 3375. Depending on your calculator, you can use the^3

√

x
function or∧

( 1

3

)

. The cubed root is the inverse of cubing a number, just like the square root is the inverse, or how
you undo, the square of a number.

√ (^33375) = 15 =r The radius is 15f t.
Practice

1. Are there any cross-sections of a sphere that are not a circle? Explain your answer.

Find the surface area and volume of a sphere with: (Leave your answer in terms ofπ)