1. Geometry Formulas:
Surface Area & Volume

2. A formula is just a set of instructions
A formula is just a set of instructions. It tells you exactly what to do!
All you have to do is look at the picture and identify the parts.
Substitute numbers for the variables and do the math. That’s it! 

3. Either method will gve you the same answer.
Let’s start with a rectangular prism.
Surface area can be done using the formula
SA = 2 lw + 2 wl + 2 lw OR
Either method will gve you the same answer.
you can find the area for each surface and add them up.
Volume of a rectangular prism is V = lwh

4. Example:
7 cm
4 cm
8 cm
Front/back 2(8)(4) = 64
Left/right 2(4)(7) = 56
Top/bottom 2(8)(7) = 112
Add them up!
SA = 232 cm²
V = lwh
V = 8(4)(7)
V = 224 cm³

5. SURFACE AREA of a CYLINDER.
Imagine that you can open up a cylinder like so:
You can see that the surface is made up of two circles and a rectangle.
The length of the rectangle is the same as the circumference of the circle!

6. EXAMPLE: Round to the nearest TENTH.
Top or bottom circle
A = πr²
A = π(3.1)²
A = π(9.61)
A = 30.2
Rectangle
C = length
C = π d
C = π(6.2)
C = 19.5
Now the area
A = lw
A = 19.5(12)
A = 234
Now add: =
SA = in²

7. There is also a formula to find surface area of a cylinder.
Some people find this way easier:
SA = 2πrh + 2πr²
SA = 2π(3.1)(12) + 2π(3.1)²
SA = 2π (37.2) + 2π(9.61)
SA = π(74.4) + π(19.2)
SA =
SA = in²
The answers are REALLY close, but not exactly the same. That’s because we rounded in the problem.

8. The formula tells you what to do!!!!
Find the radius and height of the cylinder.
Then “Plug and Chug”…
Just plug in the numbers then do the math.
Remember the order of operations and you’re ready to go.
The formula tells you what to do!!!!
2πrh + 2πr² means multiply 2(π)(r)(h) + 2(π)(r)(r)

9. Cylinder V = (πr²)(H) Volume of Prisms or Cylinders
You already know how to find the volume of a rectangular prism: V = lwh
The new formulas you need are:
H = the height of the cylinder
Cylinder V = (πr²)(H)

10. V = (πr²)(H) V = (π)(3.1²)(12) V = (π)(3.1)(3.1)(12) V = 396.3 in³
Volume of a Cylinder
We used this drawing for our surface area example. Now we will find the volume.
V = (πr²)(H)
V = (π)(3.1²)(12)
V = (π)(3.1)(3.1)(12)
V = in³
optional step!

11. V = (πr²)(H) V = (π)(4²)(10) V = (π)(16)(10) V = 502.7 m³ Try one:
d = 8 m
V = (πr²)(H)
V = (π)(4²)(10)
V = (π)(16)(10)
V = m³
Since d = 8,
then r = 4
r² = 4² = 4(4) = 16

12. Here are the formulas you will need to know:
A = lw SA = 2πrh + 2πr²
A = ½ bh V = (½ bh)(H)
A = π r² V = (πr²)(H)
C = πd
and how to find the surface area of a prism by adding up the areas of all the surfaces