Surface Area and Volume: Surface Area and Volume of Prisms and Cylinders

Calculating Surface Area of a Prism

Once you have drawn the surfaces and labeled each accurately, the surface area can easily be found using what we already know.

Surface Area:

  1. Draw and label the surfaces of a figure.
  2. Find the area of each surface.
  3. Add the areas together.
  4. Label the answer with ‘square units’.  (Remember that area is always labeled ‘square units’.)


Example:
Let’s find the surface area of the rectangular prism we first looked at.  Let’s say it has dimensions L = 10 in, W = 3 in, and H = 4 in.

Rectangular box with yellow front, red top and blue side, labeled 10 by 3 by 4
Rectangular box

 

1. Draw and label the surfaces of the figure.

Sides of the box laid out flat, two yellow rectangles, two red rectangles, two blue rectangles
Sides of the box laid out flat

 

2. Find the area of each surface.

2 yellow sides:  10 by 4
A = 10(4) = 40

2 red sides: 10 by 3
A = 10(3) = 30

2 blue sides: 3 by 4
A = 3(4) = 12

3. Add the areas together.

2(yellow) + 2(red) + 2(blue) = 2(40) + 2(30) + 2(12) = 164

4. Label the answer with 'square units'.

The total surface area is 164 in².