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Question

The cost of manufacturing a semi-circular window is the cost of the glass pane together with the cost of the framing material. When ordering this window, a customer specifies the length of the base of the window, shown as l.

 

Determine the total area of glass pane needed for a window with a base length of 3 feet. Round your answer to the nearest hundredth of a square foot.

 

If the glass pane costs $23 per square foot, what's the cost of a glass pane with the window base is 3 feet? Use your answer to part a), and round to the nearest penny.

 

Determine the largest possible window you can buy if the most you can spend on the glass pane is $350. What should you specify for the base window length? Round your answer to the nearest tenth of a foot.

Answer 1

The area of the window is 1/2 the area of a full circle. The area of the circle is PIr^2. With a base of 3 feet, the radius is 1.5 feet so the area is

 

3.14159 * 2.25 / 2 = 3.53429 sq. ft.

 

The cost of the pane is 3.53429 * $23 = $81.29

 

This assumes that the window manufacturer charges for the actual amount of glass delivered to the customer and not the amount of glass used to make the window. the glass needed to make the window is 3' x 1.5' = 4.5 sq. ft. with approximately 1 sq.ft of glass waste.

 

Still assuming the cost applies only to the amount of glass delivered to the customer

$350 / $23 = 15.2174 sq.ft. of glass.

 

So we have to find the diameter of a circle whose area is 2*15.2174 = 30.4348

 

30.4348 / 3.14159 = 9.6877059 which is the square of the radius of the  circle. So the length of the base is 2 times the square root of 9.6877059

 

The base of the window can be 6.2250 feet long.

 

Use the first part of the problem to veisy that this window will cost $350.

 

 

 

Answer 2

If the base or diameter of semi circle is 3ft

radius = 1.5 ft

 Area of semicircle = 1/2(Pi x r²) = 3.536 ft ² 

Cost @ 23 per sq ft  = 3.536 x 23 = $81.32

 

in $350 the area covered will be = 350/23 = 15.28 ft²

 

= 1/2(pi R^2) = 15.28 ft²

gives R²= 15.28x2/ pi=9.73  ft ²

R = 3.12 ft

 

New base of window =6.24 ft