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
The wood area is the area increase when the shape is offset by 1. By Steiner's formula that increase is P·1 + π·1^2, where P is the inner perimeter.
Inner perimeter = 48 + 48 + 12 + (arc of semicircle) = 96 + 12 + 6π = 108 + 6π.
Frame area = (108 + 6π) + π = 108 + 7π ≈ 129.99 square inches.
So the exact answer is 108 + 7π sq in (≈130.0). None of the four listed choices match this expression (it looks like a π symbol may be missing in the choices).
Inner perimeter = 48 + 48 + 12 + (arc of semicircle) = 96 + 12 + 6π = 108 + 6π.
Frame area = (108 + 6π) + π = 108 + 7π ≈ 129.99 square inches.
So the exact answer is 108 + 7π sq in (≈130.0). None of the four listed choices match this expression (it looks like a π symbol may be missing in the choices).
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