Question
A rectangular piece of poster board measures 60 centimeters
by 80 centimeters. Linn draws the net of a box on the poster board
and cuts it out. If the box measures 10 centimeters by 16 centimeters
by 27 centimeters, what is the area of the poster board left?
by 80 centimeters. Linn draws the net of a box on the poster board
and cuts it out. If the box measures 10 centimeters by 16 centimeters
by 27 centimeters, what is the area of the poster board left?
Ask by Hobbs Gardner. in the United States
Mar 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The area of the poster board left is 3076 square centimeters.
Solution
The area of the poster board is
The box has dimensions
where
First, compute the areas of the three distinct faces:
Add these to get:
Then, the total surface area of the box is
The poster board left after cutting out the net is the difference between the board’s area and the net’s area:
Thus, the area of the poster board left is
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To find the area of the poster board left after cutting out the net of the box, first calculate the area of the entire poster board. The area is given by the formula length × width, so:
Area of the poster board = 60 cm × 80 cm = 4800 cm².
Next, calculate the surface area of the box. The formula for the surface area (SA) of a rectangular box is:
SA = 2(lw + lh + wh),
where l = length, w = width, and h = height. Plugging in the dimensions of the box:
SA = 2(10 cm × 16 cm + 10 cm × 27 cm + 16 cm × 27 cm)
= 2(160 cm² + 270 cm² + 432 cm²)
= 2(862 cm²)
= 1724 cm².
= 2(160 cm² + 270 cm² + 432 cm²)
= 2(862 cm²)
= 1724 cm².
Finally, subtract the surface area of the box from the area of the poster board to find the area left:
Area left = 4800 cm² - 1724 cm² = 3076 cm².
So, the area of the poster board left is 3076 square centimeters.
