SOLUTION: Bill has a sheet of cardboard with an area of 10 square feet. He makes the entire sheet of cardboard into a closed rectangular box. The four sides of the box have the same area,
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Question 64009: Bill has a sheet of cardboard with an area of 10 square feet. He makes the entire sheet of cardboard into a closed rectangular box. The four sides of the box have the same area, and the two ends have the same area. The area of each of the four equial sides is twice the area of each end. What is the area of each face of Bill's box? What are the dimensions of Bill's box? How many unit cubes would it take to fill the box?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Bill has a sheet of cardboard with an area of 10 square feet. He makes the entire sheet of cardboard into a closed rectangular box. The four sides of the box have the same area, and the two ends have the same area. The area of each of the four equial sides is twice the area of each end. What is the area of each face of Bill's box? What are the dimensions of Bill's box? How many unit cubes would it take to fill the box?
:
It says that the 4 sides have equal area, therefore, we know that the ends are
square. Let x = one side of the end. The area of the end would be x^2
:
It said that the area of the sides is twice the area of the end so it's area
would be 2x^2.
:
Area of two ends + area of the four sides = 10 sq ft
2(x^2) + 4(2x^2) = 10
2x^2 + 8x^2 = 10
10x^2 = 10
x^2 = 1
x = 1 ft
The ends are 1 ft by 1 ft, (Area of 1 Sq ft)
:
The sides have an area of 2 sq ft, (twice the area of the ends as it says)
The height of the sides has to be 2 ft then, (2*1 = 2 sq ft):
:
The dimensions of the box: 1 * 1 * 2 ft = 2 cu ft volume
:
Check: 2(1) + 4(2) = 10 sq ft
:
Did this all make sense?
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