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
- Find the surface area of the figure below.
- The surface area of a sphere is 100πin^2. What is the radius?
- A sphere has a volume of 14137. 167 f t^3 , what is the radius?
Answers:
- 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
- Plug in what you know to the formula and solve forr.
100 π= 4 πr^2
25 =r^2
5 =r
- 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
- 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)