SOLUTION: What are the dimensions of a rectangular prism with a volume of 576 cubic m if the width is 3/4 the length and the height is twice the width?

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Question 772990: What are the dimensions of a rectangular prism with a volume of 576 cubic m if the width is 3/4 the length and the height is twice the width?
Answer by pakhi(24) (Show Source):
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A rectangular prism is one which has two rectangles as its two end faces.
Volume of a rectangular prism is given by the formula
Volume(V) = Area(A) of one of its rectangles * Height(H) of the prism
Let the length of the rectangle be 'L' meters
Let the width of the rectangle be 'W' meters
Then the area(A) of the rectangle is = length * width = LW square meters
But from the problem we find that W = (3/4)L
Also the height(H) of the prism = 2W = 2*(3/4)L = (3/2)L
So the volume(V) = A * H = L * (3/4)L * (3/2)L = (9/8)L^3
But V = 576 cubic meters
So (9/8)L^3 = 576
or L^3 = 576 * (8/9) = 64 * 8
or L * L * L = 8 * 8 * 8
or L = 8 meters
So W = (3/4)L = (3/4)8 = 6 meters
So H = (3/2)8 = (3/2)8 = 12 meters
Therefore the dimensions of the rectangular prism are
Length = 8m
Width = 6m
Height = 12m

Check: V = A * H = L * W * H = 8 * 6 * 12 = 576