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Chapter 10: Problem 50

A stained glass window is to be placed in a house. The window consists of a rectangle, 6 feet high by 3 feet wide, with a semicircle at the top. Approximately how many feet of stripping, to the nearest tenth of a foot, will be needed to frame the window?

Short Answer

Expert verified
The total length of stripping needed to frame the window is found by calculating the perimeters of the rectangle portion and the semicircle portion, and adding them together.

Step by step solution

01

Compute the rectangle's perimeter

The rectangle is 6 feet high and 3 feet wide. However, only the height and one side, not the full rectangle, contribute to the frame. Therefore, the portion of the frame from the rectangle can be calculated as \(6+3=9 \) feet.
02

Compute the semicircle's perimeter

The top of the window is a semicircle with the diameter equal to the width of the rectangle which is 3 feet. Hence its radius is \(r = 3/2\) feet. The perimeter of a circle is given by \( P = 2\pi r\). Therefore, the perimeter of a semicircle equals \( P = \pi r\). Substituting the value of the radius we get, \( P = \pi \times 3/2\). We calculate this to get the semicircle's perimeter.
03

Calculate the total perimeter

The total perimeter of the stained glass window is the sum of the rectangle's portion of the perimeter and the semicircle's perimeter. We add the results from step 1 and step 2 to calculate this.

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