Hello everybody and thank you so much again for all your wonderful help! I am wondering if someone could please look over my work and tell me where I went wrong? First photo attached is the question I'm working on and the second photo is my work. My textbook says my answer should be "about 21.9m^2" however my total surface area only equals 20.4m, without even subtracting the overlap! Thank you very much
Surface Area (Again)
- Thread starter Amuziart
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Hi! Thank you for your response. How do I get to 21? My entire surface area only equals 20.4. Also, how do you know when to subtract the overlap and when not to? I have some questions that make me subtract 2x the overlap, some that make me only subtract the overlap once and some that don't! How do I know ?!
Dr.Peterson
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It looks like you missed the bottom surface of the prism! Add that, and don't round too soon, and you'll have the answer.
But what skeeter suggested amounts to realizing that you can remove the circle in that bottom surface and put it on the bottom of the cylinder, using only the lateral surface of the cylinder.
The basic trick for knowing what to subtract lies in thinking about how you would actually make the object.
skeeter
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two triangular faces, [MATH]A = 6[/MATH]three rectangular faces, [MATH]A = 8[/MATH]lateral surface area of the cylinder, [MATH]A = 2\pi \cdot r \cdot h = \dfrac{5\pi}{2}[/MATH]
total surface area = [MATH]6 + 8 + \dfrac{5\pi}{2} = 21.85398163... \approx 21.9[/MATH]
the overlap between the prism and the top of the cylinder, counted once, takes care of the cylinder bottom
total surface area = [MATH]6 + 8 + \dfrac{5\pi}{2} = 21.85398163... \approx 21.9[/MATH]
the overlap between the prism and the top of the cylinder, counted once, takes care of the cylinder bottom