A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 22ft long and 16ft wide. If the gardener wants to build a fence around the garden, how many feet of fence are required? (Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.)
Question
A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 22ft long and 16ft wide. If the gardener wants to build a fence around the garden, how many feet of fence are required? (Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.)
Solution
The question doesn't provide a diagram, but based on the description, we can assume that the diameter of the semicircle is the same as the width of the rectangle, which is 16ft.
Step 1: Calculate the perimeter of the rectangle. The formula for the perimeter of a rectangle is 2(length + width). However, since one side of the rectangle is joined with the semicircle, we only need to add the length and twice the width. So, the perimeter of the rectangle part is 22ft + 2*16ft = 54ft.
Step 2: Calculate the circumference of the semicircle. The formula for the circumference of a circle is 2πr, where r is the radius. Since we have a semicircle, we will take half of the circumference. The radius of the semicircle is half of the diameter, so r = 16ft/2 = 8ft. Therefore, the circumference of the semicircle is 1/2 * 2πr = πr = 3.14 * 8ft = 25.12ft.
Step 3: Add the perimeter of the rectangle and the circumference of the semicircle to get the total length of the fence required. So, the total length of the fence required is 54ft + 25.12ft = 79.12ft.
Therefore, the gardener needs 79.12ft of fence to build around the garden.
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