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A shipping comapny is designing new cardboard packages to sell to customers.  The options are a rectangular prism, Box A, or a triangular prism, Box B.  Which box is made with less cardboard?

 

 Apr 11, 2020
 #1
avatar+930 
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An area of a prism is the area of the base time the height. Box A's area is just 4 * 10 * 3= 120in^3. Box B's area is the area of the base triangle (8/2) * 3= 12 times the height 6, so 12 * 6= 72in^3. Since 120>72, Box B is made of less cardboard.

 

🔥🔥🔥

 Apr 11, 2020
 #2
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good ol addition will help

(btw this is my 200th answer)

 Apr 11, 2020
 #3
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this has nothing to do with volume.

 

BOX A

2 side of 3"x4" = Side A

2 side 10"x3"= Side B

2 side 10"x4" = Side C

 

therefore

 

area of Side A + Area of Side B + Area of Side C = total carboard

 

so

 

2(3x4) + 2(10x3) + 2(10x4)

2(12)   + 2(30)     + 2(40)

24        + 60         + 80

TOTAL AREA BOX A = 164 square inches

 

BOX B

Area of a right triangle is 1/2 x base x height (can also be expressed as "0.5 x base x height" or "(base x height)/2" )

therefore

both triangular sides have 2 right trianges each.

this means we have

2 sides (0.5 x 8 x 3) x 2 which reduces to: 2 sides of 8 x 3 (beause the .5 and the 2 cancel each other out)

therefore we have in total

 

2 sides of 8 x 3

1 side of 8 x 6

2 sides 5 x 6

 

therefore

2(8 x 3) + (8 x 6) + 2(5 x 6)

2(24)    + (48)      + 2(30)

48        + 48         + 60

TOTAL AREA BOX B = 156 square inches

 Apr 12, 2020

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