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Answer :
Final answer:
The surface areas of the objects give the amount of material used: Amy's display box requires 86.64 square inches of glass, Bennett's jersey case requires 1938 square inches of glass, each of Paul's apple cubes will be covered with 10.67 square inches of caramel, and the plastic used for Tammy's document holder is approximately 301.44 square cm.
Explanation:
To find out how much glass or plastic is used to make these items, we need to find the surfaces areas of the given shapes as it represents the amount of materials used to make them.
Amy's display box
Since the box is cube-shaped, its surface area would be 6 * (edge length)^2. So, the amount of glass used is 6 * (3.8 in)^2 = 86.64 square inches.
Bennett's jersey case
The case is in the shape of a rectangular prism. Surface area of a rectangular prism is 2lw + 2lh + 2wh. Here, l=18 in, w=3.5 in, and h=25.5 in. Therefore, the glass used is 2*18*3.5 + 2*18*25.5 + 2*3.5*25.5 = 1938 square inches.
Paul's caramel apple cubes
For the apple cubes, we also use 6 * (edge length)^2 for surface area. Edge length is given as 1 1/3 in = 4/3 in. The caramel area is 6 * (4/3 in)^2 = 32/3 = 10.67 square inches per cube.
Tammy's document holder
The document holder is cylindrical. The surface area of a cylinder is 2πrh + 2πr^2. Here, r=2 cm and h=22 cm. Therefore, the plastic used is approximately 2*3.14*2*22 + 2*3.14*(2)^2 = 301.44 square cm.
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Rewritten by : Barada
1. - Since a cube is all the same lengths on all sides you would want to find the area of one of the sides. You would do this by multiplying 3.8 by 3.8.
3.8*3.8=14.44
Since you have six faces on a cube you want to multiply this by 6.
14.44*6=86.64
So your answer for 1. is 86.64 in^2 of glass
3. Same thing as number one. Find the face of one side:
1 1/3*1 1/3 is about 1.7777
Multiply this by the six faces.
1.7777*6 is about 10.66666
So your answer for 3. is about 10.666 (repeating) in^2
4. For this one, you want to follow the surface area formula for a cylinder. Which is - A=2πrh+2πr^2
When you put all your numbers in it would look like this:
2*3.14*2*22+2*3.14*2^2
Once you do that equation you will get 301.44
So that should be your answer 301.44 cm^2
Hope this helps!
3.8*3.8=14.44
Since you have six faces on a cube you want to multiply this by 6.
14.44*6=86.64
So your answer for 1. is 86.64 in^2 of glass
3. Same thing as number one. Find the face of one side:
1 1/3*1 1/3 is about 1.7777
Multiply this by the six faces.
1.7777*6 is about 10.66666
So your answer for 3. is about 10.666 (repeating) in^2
4. For this one, you want to follow the surface area formula for a cylinder. Which is - A=2πrh+2πr^2
When you put all your numbers in it would look like this:
2*3.14*2*22+2*3.14*2^2
Once you do that equation you will get 301.44
So that should be your answer 301.44 cm^2
Hope this helps!
