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705-805 (Hard)|   Geometry|      
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jcaguirre91
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The board of directors of an arboretum is considering two options for 26 Feb 2021, 18:46
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C
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85% (hard)

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57% (03:04) correct 43% (02:55) wrong based on 131 sessions

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The board of directors of an arboretum is considering two options for building a 10-foot-wide walkway around a rectangular field that measures 100 by 300 feet. One option is to make the walkway rectangular, but the contractor has suggested that the arboretum save money by rounding the walkway's corners while maintaining its 10-foot width. If the cost of the walkway is $8 per square foot, what is the approximate cost savings of the contractor's alternative?

A. $170
B. $350
C. $690
D. $800
E. $910
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C
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The board of directors of an arboretum is considering two options for 27 Feb 2021, 04:54
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Difference in the area\(= 4*(10*10 - \frac{\pi}{4} *10*10) = 100(4-3.14) = 86\)

Savings \(= 8*86= 640+48=688 \) ~ \(690\)


jcaguirre91
The board of directors of an arboretum is considering two options for building a 10-foot-wide walkway around a rectangular field that measures 100 by 300 feet. One option is to make the walkway rectangular, but the contractor has suggested that the arboretum save money by rounding the walkway's corners while maintaining its 10-foot width. If the cost of the walkway is $8 per square foot, what is the approximate cost savings of the contractor's alternative?

A. $170
B. $350
C. $690
D. $800
E. $910
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The board of directors of an arboretum is considering two options for 27 Feb 2021, 14:11
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jcaguirre91
The board of directors of an arboretum is considering two options for building a 10-foot-wide walkway around a rectangular field that measures 100 by 300 feet. One option is to make the walkway rectangular, but the contractor has suggested that the arboretum save money by rounding the walkway's corners while maintaining its 10-foot width. If the cost of the walkway is $8 per square foot, what is the approximate cost savings of the contractor's alternative?

A. $170
B. $350
C. $690
D. $800
E. $910
Show more

We only need to look at the corners which are 10*10 squares, we cut off the edges so that we have 4 quarter-circles instead. The area of the 4 quarter-circles is a circle of radius 10, so the new area is \(\pi *10*10 \approx 314\) while the old area was 400. Therefore we saved (400 - 314)*8 = 86*8 = 640+48 = 688.

Ans: C
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The board of directors of an arboretum is considering two options for 27 Feb 2021, 15:59
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If we consider one side of walkway,
Difference in area = 100-\(\frac{1}{4}*\pi*10^2\)
=\(100(1-\frac{\pi}{4})\)
If i replace, \(\pi\) with 3 (or 3.14 with 3) then the value of it would be less than what we are calculating now

It is less than value of =\(100(1-\frac{3}{4})\) =\(25\)

All four corners, area is less than = 25*4=100 sq ft

So total cost reduction would be less than = 100*$8 = $800

Cant be D, so must be C
Answer: C
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The board of directors of an arboretum is considering two options for 05 Mar 2021, 05:23
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jcaguirre91
The board of directors of an arboretum is considering two options for building a 10-foot-wide walkway around a rectangular field that measures 100 by 300 feet. One option is to make the walkway rectangular, but the contractor has suggested that the arboretum save money by rounding the walkway's corners while maintaining its 10-foot width. If the cost of the walkway is $8 per square foot, what is the approximate cost savings of the contractor's alternative?

A. $170
B. $350
C. $690
D. $800
E. $910

We only need to look at the corners which are 10*10 squares, we cut off the edges so that we have 4 quarter-circles instead. The area of the 4 quarter-circles is a circle of radius 10, so the new area is \(\pi *10*10 \approx 314\) while the old area was 400. Therefore we saved (400 - 314)*8 = 86*8 = 640+48 = 688.

Ans: C
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TestPrepUnlimited and other members, can you help me with the figure for this question? How is the old area 400?
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The board of directors of an arboretum is considering two options for 06 Mar 2021, 18:31
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Brian123 we are ignoring the entire rectangular field (100*300 area), that part does not change. If we add a 10-foot wide walkway around the field you'll have four 10*10 squares touching the edges of the rectangular field:
Attachments

4squares.png
4squares.png [ 19.09 KiB | Viewed 3834 times ]

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The board of directors of an arboretum is considering two options for 02 Dec 2021, 00:50
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jcaguirre91
The board of directors of an arboretum is considering two options for building a 10-foot-wide walkway around a rectangular field that measures 100 by 300 feet. One option is to make the walkway rectangular, but the contractor has suggested that the arboretum save money by rounding the walkway's corners while maintaining its 10-foot width. If the cost of the walkway is $8 per square foot, what is the approximate cost savings of the contractor's alternative?

A. $170
B. $350
C. $690
D. $800
E. $910
Show more



We are asked to find the cost savings only,so focus on the corners.

Each corner is a square with side 10.
Area of corner = 100

Bring all 4 corner squares together to form a big square.
Side of big square = 20
Area of big square = 400

Inscribe a circle in this square,this will give us the area of rounded path



Radius of circle = 10
Area of circle = pi*100 = 3.14*100
Difference = 400-314 = 86

Total cost = 86*8 = 688
Ans (C)
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The board of directors of an arboretum is considering two options for 30 Aug 2023, 19:14
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