A rectangular shipping container has a volume of 2500 cubic cm. The container is 4 times as wide as it is deep, and 5cm taller than it is wide. What are the dimensions of the container?

2500 cubic cm is not a large container!

Let W=width
then
Depth=W/4
H=W+0.05
Volume
V=2500=W*(W/4)*(W+5)
=> W^3+5W^2-10000=0
Factor:
(W-20)(W^2+25W+500)=0
=>
W=width=20 cm.
W/4=depth=20/4=5 cm
W+5=height=20+5=25 cm

Check: 20*5*25=2500 cm^3 ok

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ashishdwivedilVT ashishdwivedilVT · Answer 2 · 2022-07-13T19:37:11+02:00

The depth of the container is 5 cm, width of container is 20 cm and height of container is 25 cm.

What is Volume?

Volume is defined as a capacity occupied by a three-dimensional solid shape. In any shape, it is hard to visualize but can be compared between shapes.

Let the depth of the rectangular shipping container be x cm

width be 4x cm

and height be 4x+5 cm

Now, we know that,

Volume of container = Length X width X Height

2500 = (x) X (4x) X (4x+5)

2500 = 16x³ + 20x²

16x³ + 20x² - 2500 = 0

4x³ + 5x² - 625 = 0

(x -5) ( 4x² + 25x 125) = 0

Now, either (x - 5) = 0 or 4x² + 25x 125 = 0

But, 4x² + 25x 125 = 0 is not possible because all terms are positive.

So, x - 5 = 0

x = 5

Thus, the depth of the container is 5 cm, width of container is 20 cm and height of container is 25 cm.

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