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anonymous
 one year ago
The base of a solid in the xyplane is the circle x2 + y2 = 16. Cross sections of the solid perpendicular to the yaxis are equilateral triangles. What is the volume, in cubic units, of the solid?
anonymous
 one year ago
The base of a solid in the xyplane is the circle x2 + y2 = 16. Cross sections of the solid perpendicular to the yaxis are equilateral triangles. What is the volume, in cubic units, of the solid?

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DanJS
 one year ago
Best ResponseYou've already chosen the best response.2Do you know what the solid is?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no I don't know how to start this problem

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2They gave you x^2 + y^2 = 16 = r^2 That is a circle radius 4 centered at the origin, in the XYplane...

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2bad drawing, but that is a slice of the shape perpendicular to the Y axis

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2saying it is equilateral, means that is a Right Circular Cone

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so you need the volume formula for a right circular cone correct?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2yes, just remember, it is the area of the base times 1/3 the height

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2need to figure the height

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2Loooking at the cross section at the XZ axis head on... the base is 2 times the radius

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2THe y axis is pointing out from the page, that is the origin

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2Equilateral triangle, so the diagonals are the same as the base, 2 radiuses

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2r=4, use pythagorean theorem to figure the height

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2you can only put in the 2r because they told you the cross sections are equilateral

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2pelletty drawing, but hope you see where those measurments come from

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes it is understood

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2k, so you know the radius and height, you can calculate the volume \[V = \frac{ 1 }{ 3 }\pi*r^2*h\]

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2r = 4 h = sqrt(8^2  4^2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The way you set it up is multiply 1/3 by pi(4)^2(sqrt(8^24^2))?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2yes, if you simplify the height first, it is... \[h = \sqrt{6416} = 4\sqrt{3}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay thank you very much for the explanation

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2\[V = \frac{ 1 }{ 3 }*\pi*4^2*4\sqrt{3}\]

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2welcome, that was a fun prob.. hope ya get it
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