anonymous
  • anonymous
A cube shaped block of wood has a side length of (everyone try this one).. its hard!12 centimeters. The cube has a circular hole drilled straight through its center. The radius of the hole is 3 centimeters. What is the surface area of the cube with the hole drilled through it?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
864-54pi is the surface area... that's what I got.
AccessDenied
  • AccessDenied
maybe a picture will help visualize: |dw:1332547764118:dw|
AccessDenied
  • AccessDenied
doesn't the question ask for surface area tho?

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anonymous
  • anonymous
thats volume... im looking for surface area
AccessDenied
  • AccessDenied
basically, we'd have six faces on the cube, so we take the area of all six squares... but since we made that hole, we remove that circle on both sides (the hole goes all the way through the block, so its gone from two sides) from the area of those squares (since a hole 'omits' that area from the square, its not part of the surface anymore).
AccessDenied
  • AccessDenied
not sure if you include the cylinder from the hole as part of the surface area, if so then you'd also add that surface area of the 'cylinder' that is formed by the hole, excluding the base circle
anonymous
  • anonymous
do you have any numbers i can work with?
AccessDenied
  • AccessDenied
im working through the problem myself, and then ill just put my work... :)
anonymous
  • anonymous
thanks.. i appreciate it!
AccessDenied
  • AccessDenied
Abbreviating Surface Area as "S.A.": \[ Total~S.A. = S.A.~of~Cube +S.A.~of~Cylinder-S.A.~of~2~circles,~where:\\ ~~S.A.~of~Cube=6s^2,\\ ~~S.A.~of~Cylinder=2\pi rs,~and\\ ~~S.A.~of~2~Circles=\pi r^2 + \pi r^2 = 2\pi r^2;\\ r=radius~and~s=side~length.\\~\\ Total~S.A.=6s^2 + 2\pi rs - 2\pi r^2\] \[ Using~s=12~and~r=3...\\\\ \begin{split} ~~S.A.~of~Cube&=6(12)^2\\ &=6(144)\\ &=864\\\\ \end{split}\\ \begin{split} ~~S.A.~of~Cylinder&=2\pi (3)(12)\\ &=72\pi\\\\ \end{split}\\ \begin{split} ~~S.A.~of~2~Circles&=2\pi (3)^2\\ &=2\pi (9)\\ &=18\pi\\\\ \end{split}\\ Thus;\\ \begin{split} ~Total~S.A. &= 864 + 72\pi - 18\pi\\ &= 864 + 54\pi ~cm^2~~~~~~~~~~~\pi \approx 3.14\\ &\approx 1033.56 ~cm^2\\ \end{split}\\ \]
AccessDenied
  • AccessDenied
I should probably just say "Area of 2 Circles," since circles are 2D

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