The total cost of the glass for your window now $174.8
How to determine the total cost of the glass for your window now?
The complete question is added as an attachment
From the attached figure, we have the following parameters:
- Square of side length 24 inches
- Circle B of diameter 20 inches
- Circle A of diameter 18 inches
The area of region 1 is calculated using:
Region 1 = Area of square - Area of circle B
This is calculated as
Region 1 = L^2 - π(d/2)^2
So, we have:
Region 1 = 24^2 - 3.14 * (20/2)^2
Evaluate the quotient
Region 1 = 24^2 - 3.14 * 10^2
Evaluate the exponent
Region 1 = 576 - 3.14 * 100
Evaluate the product
Region 1 = 576 - 314
Evaluate the difference
Region 1 = 262
The cost per square inch of this region is $0.10.
So, we have:
Total cost of region 1 = 262 * $0.10
Total cost of region 1 = $26.10
The area of region 2 is calculated using:
Region 2 = Area of circle B - Area of circle A
This is calculated as
Region 2 = π(D/2)^2 - π(d/2)^2
So, we have:
Region 2 = 3.14 * (20/2)^2 - 3.14 * (18/2)^2
Evaluate the quotient
Region 2 = 3.14 * 10^2 - 3.14 * 9^2
Evaluate the exponent
Region 2 = 3.14 * 100 - 3.14 * 81
Evaluate the product
Region 2 = 314 - 254.34
Evaluate the difference
Region 2 = $59.66
The cost per square inch of this region is $0.15.
So, we have:
Total cost of region 2 = 59.66 * $0.15
Total cost of region 2 = $8.949
The circle B is divided into sectors.
And the angles of the sectors are 90 and 270 degrees
The area of each sector is
Area = ∅/360 * π(d/2)^2
So, we have:
Circle B = ∅/360 * π(d/2)^2 + ⊕/360 * π(d/2)^2
So, we have:
Circle B = 90/360 * 3.14 * (18/2)^2 + 270/360 * 3.14 * (18/2)^2
Evaluate the quotient
Circle B = 0.25 * 3.14 * 9^2 + 0.75 * 3.14 * 9^2
Evaluate the exponent
Circle B = 0.25 * 3.14 * 81 + 0.75 * 3.14 * 81
Evaluate the product
Circle B = 63.585 + 190.755
The cost per square inch of this region is $0.80 for 1 sector and $0.20 for the rest
So, we have:
Total cost of circle B = 63.585 * 0.80 + 190.755 * 0.20
Total cost of circle B = 89.019
Add the total costs
Total cost of the glass for your window = Region 1 + Region 2 + Circle B
Total cost of the glass for your window = $26.10 + $59.66 + $89.019
Evaluate the sum
Total cost of the glass for your window = $174.779
Approximate
Total cost of the glass for your window = $174.8
Hence, the total cost of the glass for your window now $174.8
Read more about areas at:
https://brainly.com/question/76387
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