SOLUTION: would you please solve the following problem? Plastic Box A has a square base of area 36 cm² and a height of 8 cm. It is completely filled with juice. Plastic Box B is empty and

Algebra ->  Finance -> SOLUTION: would you please solve the following problem? Plastic Box A has a square base of area 36 cm² and a height of 8 cm. It is completely filled with juice. Plastic Box B is empty and      Log On


   

Question 1057115: would you please solve the following problem?
Plastic Box A has a square base of area 36 cm² and a height of 8 cm. It is completely filled with juice. Plastic Box B is empty and has dimensions 5 cm by 3 cm by 12 cm. Juice from Box A is poured into Box B until it is filled to the very top. Find the height of the new juice level in Box A.
-Thank you.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Volume of A: 36cm%5E2+%2A+8cm+=+288cm%5E3+
Volume of B: +5cm%2A3cm%2A12cm+=+180cm%5E3+
When A is poured into B, that "subtracts" 180cm%5E3 from A. So 288cm%5E3-180cm%5E3+=+108cm%5E3 are remaining in A. If we divide that volume by the area of the base, we'll get the height:
108cm%5E3+%2F+%2836cm%5E2%29+=+3cm+
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Ans: The juice will have a height of 3cm in box A after filling box B.
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NOTE: this problem can also be easily solved using a proportion. The 108cm%5E3 volume remaining is 3%2F8 of the original 288cm%5E3 volume so the height would be %283%2F8%29%2A+8cm+=+3cm+.