Before a space supply mission, Nova, Luna, and Emek had two rectangular containers that could hold the same equipment. Container A measured 8 meters by 3 meters by 2 meters. Container B measured 6 meters by 4 meters by 2 meters. Nova calculated the surface area of Container A as 92 square meters. Luna found that Container B had a surface area of 88 square meters. Emek checked both calculations by adding the areas of all six faces. Since protective coating was limited, they chose Container B, which needed 4 fewer square meters of coating. They covered it and prepared for launch.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Find the three different face areas, then remember that each has an identical opposite face.
Which calculation correctly checks the surface area of Container B, which measures 6 meters by 4 meters by 2 meters?
6 * 4 * 2 = 482 * (6 + 4 + 2) = 246 * 4 + 6 * 2 + 4 * 2 = 442 * (6 * 4 + 6 * 2 + 4 * 2) = 88Correct! Doubling the sum of the three different face areas gives 88 square meters.
Try again. Surface area includes all six faces of the rectangular container.
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Hint
Find the difference between the two surface areas.
Container A has a surface area of 92 square meters, and Container B has a surface area of 88 square meters. How many fewer square meters of protective coating does Container B need?
Correct! Container B needs 4 fewer square meters of coating.
Try again. Subtract the smaller surface area from the larger surface area.
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Hint
Compare what volume measures with what surface area measures.
A crew member says Container A and Container B must have the same surface area because both have a volume of 48 cubic meters. Which statement correctly explains the mistake?
Containers with the same volume can have different dimensions and different surface areas.Containers with the same volume must always have the same surface area.Surface area is found by multiplying length, width, and height.Container A has less surface area because 92 is less than 88.Correct! Equal volumes do not guarantee equal surface areas when the dimensions are different.
Try again. The containers hold the same amount, but their outside face dimensions are different.
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