Find the volume of the square pyramid shown. Round to the nearest tenth if necessary.

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Find the volume of the square pyramid shown. Round to the nearest tenth if necessary.

Mathematics
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@phi I would know how to do this if it wasn't for the slant height. How do I make it a regular height?
1 Attachment
  • phi
|dw:1441659885410:dw|
  • phi
|dw:1441659931267:dw|

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Other answers:

  • phi
not my best drawing. but the idea is the height from the top to the base lands exactly in the center of the square. the distance to a side is 1/2 the distance across, so 5
  • phi
if we concentrate on the triangle |dw:1441660064080:dw|
So 5 squared + 13 squared = h squared? That would be 194 = h squared. DO I dived 194 by 2 now?
divide*
  • phi
in \[ a^2 + b^2 = c^2 \] c is *always* the hypotenuse (the longest side) in this problem, the 13 is the hypotenuse
Oh ok. I should've known that. Lol. So h squared + 5 squared = 13 squared. (I don't know how to put the equation on here)
  • phi
you could type h^2 +5^2 = 13^2 5^2 means 5*5 13^2 means 13*13
Ok. Thanks! Lol and then once you solve that you do it exactly like the last problem we did?
  • phi
yes. what do you get for h^2 ?
h^2+5^2=13^2 h^2=13^2-5^2 h^2=144 144/2=72 Did I do that right?
  • phi
h^2=144 ok. now take the square root of both sides. (h^2/2 does not "undo" the square)
  • phi
the idea is \( \sqrt{h^2 } =h \) so we do that to both sides
I did the sqare root of 144 on my calcalator and I got 12.
  • phi
yes, h=12 as a check you can do 5^2 + 12^2 and it should give 13^2 (and it does)
  • phi
btw, (some) people memorize 3,4,5 as forming a right triangle (5 is the hypotenuse) and also 5,12,13 is a right triangle. there are lots more, but these two show up on tests a lot.
Ok I have one more question to post. I hope I'm not bothering you!
  • phi
what did you get for the volume. (it would be a shape to make a mistake now)
1200?
  • phi
what is the formula for the volume of a pyramid?
1/3BH
  • phi
put in numbers for B and h
Oh it's 400. I forgot to put the 1/3 when I first did it
  • phi
yes, 400
That would have been a simple mistake lol Thanks

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