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deff fn [24]
3 years ago
5

A student builds a model of a high-rise for a diorama for an architecture class. The model is a perfect cube and the total volum

e is 500 cubic centimeters. How long is one side of the high-rise building? (Recall that the volume of a cube is calculated by l3 , where l is the length of one side).
Mathematics
2 answers:
laila [671]3 years ago
6 0
The answer is 166.6666667
BartSMP [9]3 years ago
3 0
Volume of the cube (V) = 500cm^3
V = side/length (l)^3 --> so length of one side (l) = cube root (cr) of 500cm^3
This can be done on a calculator by using 500^(1/3), since fractional exponents represent roots:
l = crV = cr500cm^3 = 7.937
= 7.94 cm
* you can verify this by cubing 7.94
--> 7.94^3 = ~500
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Let

x------> the length of the rectangle

y------> the width of the rectangle

we know that

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see the draw in the attached figure N 1

<u>case 2)</u> For x=32 units

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y=64/x

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see the draw in the attached figure N 2

<u>case 3)</u> For x=16 units  

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x*y=64

y=64/x

y=64/16

y=4\ units

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see the draw in the attached figure N 3

<u>case 4)</u> For x=30 units

substitute in the equation 1

x*y=64      

y=64/x

y=64/30

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see the draw in the attached figure N 4

<u>case 5)</u> For x=40 units

substitute in the equation 1

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y=64/x

y=64/40

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see the draw in the attached figure N 5

<u>case 6)</u> For x=60 units

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y=64/x

y=64/60

y=\frac{16}{15} =1\frac{1}{15} \ units

the dimensions of the rectangle are 60 units x 1 (1/15) units

see the draw in the attached figure N 6

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