Geometry Problem Solving Paper

Published: 2017-11-15 08:53:35
265 words
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University/College: 
Carnegie Mellon University
Type of paper: 
Problem solving
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Total Surface Area Working

 

 

Rectangular Prism

 

Right Circular Cylinder

Right Circular Cone

Sphere

Volume Formula

V=whl

V=πr2h

V=πr2h/3

V=4/3πr3

 

1560 in3

1539.38 m3

1507.96

1500 in3

Total surface area formula

TSA = 2(lw + lh + wh)

TSA=2πrh+2πr2

TSA=πrs + πr2

TSA = 4πr2

 

 

l = 10 in
w = 13 in
h = 12 in
d = 20.3224 in
S = 812 in2
V = 1560 in3

r = 7 m
h = 10 m
V = 1539.38 m3
L = 439.823 m2

T = 153.938 m2

r = 12 in
h = 10 in
s = 15.6205 in
V = 1507.96 in3
L = 588.879 in2
B = 452.389 in2
A = 1041.27 in2

r = 7.3 in
V = 1630 in3
A = 670 in2
C = 45.9 in

TSA

=812 in2

=747.699 m2

= 1041.27 in2

= 670 in2x

Area of bottom

=130 in2

= 154 in2

= 452 in2

= 670 +670+167 in2

=1674 in2

Total area

=942 in2

=901.7 in2

=1493.27 in2

=837 in2

Key

l = length
w = width
h = height

r = radius
h = height
V = volume
L = lateral surface area

r = radius
h = height
s = slant height

 

Calculation for cost

 

 

Rectangular Prism

 

Right Circular Cylinder

Right Circular Cone

Sphere

Cheapest material

Total area

=942 in2

=901.7 in2

=1493.27 in2

=837 in2

 

Wood - $3.06 per square foot

 

6.542X3.06 =20.019

6.26X3.06

= 19.16

10.37 x 3.06

= 31.732

11.63 X3.06=35.573

Wood/ right circular cylinder

Plastic - $23.97 per square yard

 

0.73 X23.97=17.5

0.12X23.97

=16.78

1.16 X 23.97

=27.619

1.3X23.97

=31.161

Plastic /Right Circular Cylinder

Aluminum - $0.02 per square inch

 

942 X0.02

=18.84

901.7X0.02

= 18.03

1041.27X0.02

= 29.865

1674X0.02

=33.48

Aluminum/ Right Circular Cylinder

Stainless Steel - $35.46 per square meter

0.6077407X35.46=  21.55

0.581 X35.46 

=  20.63

0.67X35.46

=34.162

1.078 x 35.46

= 38.297

Stainless Steel /Right Circular Cylinder

 

 

 

 

 

 

 

Conclusion 

Total cost of plastic container with right circular cylinder shape is only $16.78, compared to Aluminum $18.03, and Stainless Steel $20.63, or wood $ 19.16.

Recommendation

The company should choose plastic material and make them in the shape of Right Circular Cylinder because it is the cheapest and costs only $16.78 per container.

sheldon

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