anonymous
  • anonymous
The base of a solid in the xy-plane is the circle x2 + y2 = 16. Cross sections of the solid perpendicular to the y-axis are equilateral triangles. What is the volume, in cubic units, of the solid?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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DanJS
  • DanJS
Do you know what the solid is?
anonymous
  • anonymous
no I don't know how to start this problem
DanJS
  • DanJS
|dw:1438722075391:dw|

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More answers

DanJS
  • DanJS
They gave you x^2 + y^2 = 16 = r^2 That is a circle radius 4 centered at the origin, in the XY-plane...
DanJS
  • DanJS
you recognize that?
anonymous
  • anonymous
yes
DanJS
  • DanJS
|dw:1438722233544:dw|
DanJS
  • DanJS
bad drawing, but that is a slice of the shape perpendicular to the Y axis
DanJS
  • DanJS
saying it is equilateral, means that is a Right Circular Cone
anonymous
  • anonymous
okay so you need the volume formula for a right circular cone correct?
DanJS
  • DanJS
yes, just remember, it is the area of the base times 1/3 the height
anonymous
  • anonymous
ok
DanJS
  • DanJS
need to figure the height
DanJS
  • DanJS
Loooking at the cross section at the XZ axis head on... the base is 2 times the radius
DanJS
  • DanJS
|dw:1438722512573:dw|
DanJS
  • DanJS
THe y axis is pointing out from the page, that is the origin
DanJS
  • DanJS
Equilateral triangle, so the diagonals are the same as the base, 2 radiuses
DanJS
  • DanJS
radii
DanJS
  • DanJS
r=4, use pythagorean theorem to figure the height
DanJS
  • DanJS
|dw:1438722659628:dw|
DanJS
  • DanJS
You get it all?
anonymous
  • anonymous
yes so far
DanJS
  • DanJS
|dw:1438722796113:dw|
DanJS
  • DanJS
you can only put in the 2r because they told you the cross sections are equilateral
DanJS
  • DanJS
|dw:1438722884153:dw|
DanJS
  • DanJS
pelletty drawing, but hope you see where those measurments come from
anonymous
  • anonymous
yes it is understood
DanJS
  • DanJS
k, so you know the radius and height, you can calculate the volume \[V = \frac{ 1 }{ 3 }\pi*r^2*h\]
DanJS
  • DanJS
r = 4 h = sqrt(8^2 - 4^2)
anonymous
  • anonymous
The way you set it up is multiply 1/3 by pi(4)^2(sqrt(8^2-4^2))?
DanJS
  • DanJS
yes, if you simplify the height first, it is... \[h = \sqrt{64-16} = 4\sqrt{3}\]
anonymous
  • anonymous
okay thank you very much for the explanation
DanJS
  • DanJS
\[V = \frac{ 1 }{ 3 }*\pi*4^2*4\sqrt{3}\]
DanJS
  • DanJS
welcome, that was a fun prob.. hope ya get it

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