Unit 11 Review: Surface Area
And Volume of Solids
By: John Prisby and Rithik Palani
Definitions
Volume: The amount of space that an object
takes up
Surface Area: The area of all the faces of an
object
Lateral Area: The surface area of an object
excluding the area of the bases
Surface Area Formulas
Cylinder
Cone
Lateral Area
Sphere
2πrh
πrl
None
Surface Area
4πr²
2πrh+2πr²
πrl+πr ²
Volume Formulas
Cylinder/Prism
Sphere
B x h ( πr²h)
Cone/Pyramid
⅓Bxh
4/3 πr3
Common Mistakes
❖ Forgetting to add bases when solving for surface area
❖ Using 4/3πr² instead of 4/3πr³
❖ When solving for a prism, using the slant height instead of
the height
❖ Not adding the base to a hemisphere when finding surface
area
Connection to other units
● Our unit is similar to unit 10 because
you have to find the area of 2-D.
However, you have to find 3-D solids
in Unit 11 in addition to 2-D shapes.
Problem #1
4 in.
2 in.
8 in.
Find the surface area of the
prism shown.
Solution
SA:2(4*2)+2(4*8)+2(8*2)
2(8)+2(32)+2(16)
16+64+32
112
Problem #2
Question
Solution
πr²h
Volume:
8
π(8)²(12)
12
π(64)(12)
768π
Find the surface area and
volume of this cylinder.
2πrh+2πr²
2π(8)(12)+2π(8)²
Surface Area:
Problem #3
Question
Solution
V=πr2h+1/3πr2h
π(12)(11)+1/3π(12)(2)
11π+2/3π
11⅔π
Find the volume of the combination of
shapes shown.
Real Life Situation
a. Imagine you are trying to figure out how much your
garbage can can hold. Find the volume of the trash can.
b. You also want to paint the can black. Find the surface
area of the cylinder.
8
16