SOLUTION: Find the dimensions of a rectangular prism with a volume of 162 cubic m if the width is 1/2 the length and the height is three times the width.

Question 772989: Find the dimensions of a rectangular prism with a volume of 162 cubic m if the width is 1/2 the length and the height is three times the width.
Answer by pakhi(24) (Show Source): You can put this solution on YOUR website!
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 = (1/2)L
Also the height(H) of the prism = 3W = 3*(1/2)L = (3/2)L
So the volume(V) = A * H = L * (1/2)L * (3/2)L = (3/4)L^3
But V = 162 cubic meters
So (3/4)L^3 = 162
or L^3 = 162 * (4/3) = 54 * 4 = 2 * 27 * 4
or L * L * L = 2 * 2 * 2 * 3 * 3 * 3
or L = 6 meters
So W = (1/2)L = (1/2)6 = 3 meters
So H = (3/2)L = (3/2)6 = 9 meters
Therefore the dimensions of the rectangular prism is
Length = 6m
Width = 3m
Height = 9m

Check: V = A * H = L * W * H = 6 * 3 * 9 = 162

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