SOLUTION: A stained-glass window is being designed in the shape of a rectangle surmounted by a semicircle, as shown in the figure. The width of the window is to be 3 feet, but the height h
Algebra ->
Customizable Word Problem Solvers
-> Geometry
-> SOLUTION: A stained-glass window is being designed in the shape of a rectangle surmounted by a semicircle, as shown in the figure. The width of the window is to be 3 feet, but the height h
Log On
Question 121588This question is from textbook algebra and trigonometry with analiytic geometry
: A stained-glass window is being designed in the shape of a rectangle surmounted by a semicircle, as shown in the figure. The width of the window is to be 3 feet, but the height h is yet to be determined. If 23 ft 2 of glass is to be used, find the height h.
Please round the answer to the nearest hundredth.
Enter your answer as a number without the units. This question is from textbook algebra and trigonometry with analiytic geometry
You can put this solution on YOUR website! You don't say whether the height is from the bottom of the window to the top of the semi-circle, or just the height dimension of the rectangle.
Since the semi-circle sits on top of the rectangle of width 3, the radius of the semi-circle must be 1.5. The area of the semi-circle is then
If we let h be the height of the rectangle, then the area of the rectangle must be 3x.
The entire area, given as , must be the sum of these two areas or:
Using 3.14 and rounding at the end:
Remember, this is the height of just the rectangle. If you need the overall height of the figure, you just need to add one circle radius, 1.5, to your answer to get
