How many square inches of plastic did Terry use before cutting the hole?
Understand the Problem
The question is asking how much plastic was used to create a birdhouse, given its dimensions. To solve this, we will calculate the surface area of the birdhouse before any holes are cut out.
Answer
The total surface area of the birdhouse is \( 376 \) square inches.
Answer for screen readers
The total surface area of the birdhouse is ( 376 ) square inches.
Steps to Solve
- Identify the shape and dimensions The birdhouse is a rectangular prism with dimensions:
- Length (l) = 10 inches
- Width (w) = 8 inches
- Height (h) = 6 inches
- Calculate the surface area The formula for the surface area $A$ of a rectangular prism is given by: $$ A = 2lw + 2lh + 2wh $$
Substituting the dimensions into the formula:
- $lw = 10 \times 8 = 80$
- $lh = 10 \times 6 = 60$
- $wh = 8 \times 6 = 48$
Calculating the surface area: $$ A = 2(80) + 2(60) + 2(48) $$
- Perform the calculations Calculating each term:
- $2(80) = 160$
- $2(60) = 120$
- $2(48) = 96$
Add these values together: $$ A = 160 + 120 + 96 $$
- Final surface area result Calculating the total: $$ A = 376 \text{ square inches} $$
The total surface area of the birdhouse is ( 376 ) square inches.
More Information
This calculation gives the total surface area for the birdhouse made from plastic before any modifications, such as cutting holes, are made. Understanding how to apply the surface area formula for a rectangular prism is essential in practical applications such as construction or crafts.
Tips
- Forgetting to double each area calculation (like $lw$, $lh$, and $wh$) when using the surface area formula. Always remember to multiply by 2 for each pair of dimensions.
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