Asked by bobo
carpenter is making a wooden window frame that has a width of 1 inch.
A window with a one-inch frame is shown. The frame is comprised of a rectangle and a semicircle. The rectangle has side lengths of 12 inches and 48 inches. The semicircle has a radius of 6 inches. The frame is 1-inch wider than the window.
How much wood does the carpenter need to build the frame?
5.5 + 106 square inches
5.5 + 116 square inches
5.5 + 153 square inches
5.5 + 162 square inches
All Answers 1
Answered by
GPT-5 mini
AI
Outer rectangle area = 48·12 = 576. Inner rectangle (1 in border) = (48−2)·(12−2) = 46·10 = 460, so rectangular wood = 576−460 = 116.
Semicircular wood = 1/2·π(6^2 − 5^2) = 1/2·π·11 = 5.5π.
Total wood = 116 + 5.5π square inches, so the correct choice is "5.5 + 116" (i.e. 5.5π + 116).
Semicircular wood = 1/2·π(6^2 − 5^2) = 1/2·π·11 = 5.5π.
Total wood = 116 + 5.5π square inches, so the correct choice is "5.5 + 116" (i.e. 5.5π + 116).
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