SOLUTION: the volume of a rectangular pool is 1,080 cubic meters. its length, width, and depth are in the ratio 10:4:1. find the number of meters in each of the three dimensions of the pool.

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Question 168680: the volume of a rectangular pool is 1,080 cubic meters. its length, width, and depth are in the ratio 10:4:1. find the number of meters in each of the three dimensions of the pool.
Answer by Earlsdon(6098) About Me  (Show Source):
You can put this solution on YOUR website!
The length (L), width (W), and depth (D) are in the ratio of 10:4:1.
The volume is given as 1080 cu meters.
The formula for the volume of the pool ( a rectangular prism) is:
V+=+L%2AW%2AD Substitute V = 1,080, L = 10x, W = 4X, and D = x.
1080+=+%2810x%29%284x%29%28x%29 Multiply.
1080+=+40x%5E3 Divide both sides by 40.
27+=+x%5E3 Take the cube root of both sides.
x+=+3
The length (L) is 10(3) = 30 meters.
The width (W) is 4(3) = 12 meters.
The depth (D) is 1(3) = 3 meters.
Check:
V+=+L%2AW%2AD
V+=+30%2A12%2A3
V+=+360%2A3
V+=+1080Cu.meters.