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Over [174]
1 year ago
5

Corbin made a scale model of the San Jacinto Monument. The monument has an actual height of 604 feet. Corbin's model used a scal

e in which 1 inch represents 100 feet. What is the height in inches of Corbin's model?
Mathematics
1 answer:
photoshop1234 [79]1 year ago
8 0

<u>Answer: </u><u>6.04 inches</u>

<u>Step-by-step explanation:</u>

The actual height of the monument = 604 feet

The scale used by Corbins is 1 inch = 100 feet

The height of the Corbins model in inches= \frac{604}{100} = 6.04 inches

the height of the Corbins model = 6.04 inches

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Part I
We have the size of the sheet of cardboard and we'll use the variable "x" to represent the length of the cuts. For any given cut, the available distance is reduced by twice the length of the cut. So we can create the following equations for length, width, and height.
width:  w = 12 - 2x
length: l = 18 - 2x
height: h = x

Part II
v = l * w * h
v = (18 - 2x)(12 - 2x)x
v = (216 - 36x - 24x + 4x^2)x
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Part III
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Let's try to figure out an x that gives a volume of 224 in^3. Since this is high school math, it's unlikely that you've been taught how to handle cubic equations, so let's instead look at integer values of x. If we use a value of 1, we get a volume of:
v = 4x^3 - 60x^2 + 216x
v = 4*1^3 - 60*1^2 + 216*1
v = 4*1 - 60*1 + 216
v = 4 - 60 + 216
v = 160

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v = 224

And that's the desired volume.
So let's choose a value of x=2.
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It meets the inequality of 0 < x < 6 and it also gives the desired volume of 224 cubic inches.
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