SOLUTION: The inside dimensions of a trunk are 5 ft., 4ft.,3 ft. Find the dimensions of a trunk similar in the shape that will hold 6 times as much. Pls. can anyone help me?

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Question 1193434: The inside dimensions of a trunk are 5 ft., 4ft.,3 ft. Find the dimensions of a trunk similar in the shape that will hold 6 times as much.
Pls. can anyone help me?
Found 2 solutions by Alan3354, Boreal:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
The inside dimensions of a trunk are 5 ft., 4ft.,3 ft. Find the dimensions of a trunk similar in the shape that will hold 6 times as much.
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Each dimension must be multiplied by the same factor for similarity.
For 6 times the volume, the factor is
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To get 8 times the volume, each dimension would be doubled.

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
the new trunk has to have volume 360 ft^2. Let x=the amount that has to be added in feet.
the dimensions will be (5+x)(4+0.8x)(3+0.6x), to keep the same shape.
This is 0.48x^3+7.2x2+36x+60=360
I get the 0.8 because the width is 4/5 of the length. This gives the same result as the cube root of 6. So 0.8x/1x is 4/5 and 0.6 to 1 x is 3/5 and 3/4 compared to the other.
x=4.086 ft.
the dimensions are 9.086 ft*7.2686 ft.*5 4516 ft.=360.04 ft^3