Saving Your Money with Surface Area

Student Sample

By Stephanie Lee

Goal

By the end of this presentation, you will know how to use surface area to save you money! Here is our scenario:

Your dog needs a new doghouse. Your parents agreed to buy the doghouse, but you are responsible for buying the paint and painting it. You want to save as much money on buying paint as possible. Where do you go to buy paint, and how much of it do you buy?

Questions to Consider

• What solid figures make up a dog house?• Are there any faces of the solids you won’t

need to paint? • What are the dimensions of the dog house?

• What are the formulas for computing the surface area of the solids?

• Where would you need to go to find information on the price of paint?• Does the color of paint matter?

• The doghouse is made up of a prism and a pyramid.

• The prism’s measurements:• Length (l)= 3 ft.• Width (w)= 3 ft.• Height (h)= 3 ft.

• The pyramid’s measurements:• Length of base (s) = 3 ft.• Slant Height (l) = 2.5 ft.

Step 1: The Doghouse

Step 2: The Formulas

Surface area of Prism:

SA = 2(lw + lh + wh)

Surface area of Pyramid:

SA = s² + 4(½sl)

http://www.mathguide.com/lessons/SurfaceArea.html

Step 3: Substitute & Solve

Surface area of Prism:

SA = 2(lw + lh + wh)SA = 2[(3)(3)+(3)(3)+(3)(3)]

SA = 2(9+9+9)

SA = 2(27)

SA = 54 ft.²

Surface area of Pyramid:

SA = s² + 4(½sl)SA = (3)²+4[½(3)(2.50]

SA = 9+4[½(7.5)]

SA = 9+4(3.75)

SA = 9+15

SA = 24 ft.²

Step 4: Subtract Unnecessary Area

Because the prism and pyramid are attached together, there are certain sides to each solid that are not painted.

• The top of the prism is not painted.• The bottom of the pyramid is not painted.

Therefore, you must subtract the area of these two sides from their respective surface area:

• Prism SA = 54ft.² ; 54 – (3)(3) = 45ft.² • Pyramid SA = 24 ft.² ; 24 – (3)² = 15ft.²

Step 5: Add Surface Areas Together

• Prism SA = 45ft.²

• Pyramid SA = 15ft.²

SATotal = SAPrism + SAPyramid

SATotal = 45 + 15

SATotal = 60ft.²

What Now?Now that we’ve found the total area of the

doghouse that needs to be painted, we need to research the cost of paint. As we research, we need to look for three things:

1.The cost of a can of paint in different stores.

2.How much can be painted with a can of paint?

3.Any price differences in color.

Step 6: The Research

• We visited the websites of two competing stores that carry paint • Home Depot and Lowes.

• We looked for a product that both stores carried• KILZ 2 Pigmented Interior/Exterior Water-

Based Sealer-Primer-Stainblocker in white

• We looked for differences in paint color

Step 7: The Results

• A quart of KILZ 2 Pigmented Interior/Exterior Water-Based Sealer-Primer-Stainblocker in white is cheaper at Home Depot by $.49.• Home Depot Price = $6.98

• Lowe’s Price = &7.47

• A gallon of paint can be used to paint between 375-400ft².

• Therefore, a quart of paint can cover between 93.75-100ft.² (1 gallon = 4 quarts).

• You only need to paint 60ft.², so 1 quart of paint is more than enough.

Step 7: The Results (continued)

• Paint color seems to have an impact on price• When the only difference between the paints within a

store was the color, white paint was less expensive.• Depending on the brand of paint, darker colors would

be more expensive than lighter colors or vice versa.• Store specials labeled only select colors as on sale

while other colors remained at regular price.

• The difference in prices of colored paint versus white paint between stores was not compared.• The same color and brand weren’t always sold in both

stores.

Resources & Work Cited

• MathGuide Website• Home Depot's Paint Pricing for KILZ Paint• Lowe's Paint Pricing for KILZ Paint• Gallon of Paint Productivity Calculator