Question

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?

Answer 1

Do you know what the solid is?

Answer 2

no I don't know how to start this problem

Answer 3

They gave you x^2 + y^2 = 16 = r^2

That is a circle radius 4 centered at the origin, in the XY-plane...

Answer 4

you recognize that?

Answer 5

yes

Answer 6

bad drawing, but that is a slice of the shape perpendicular to the Y axis

Answer 7

saying it is equilateral, means that is a Right Circular Cone

Answer 8

okay so you need the volume formula for a right circular cone correct?

Answer 9

yes, just remember, it is the area of the base times 1/3 the height

Answer 10

ok

Answer 11

need to figure the height

Answer 12

Loooking at the cross section at the XZ axis head on... the base is 2 times the radius

Answer 13

THe y axis is pointing out from the page, that is the origin

Answer 14

Equilateral triangle, so the diagonals are the same as the base, 2 radiuses

Answer 15

radii

Answer 16

r=4, use pythagorean theorem to figure the height

Answer 17

You get it all?

Answer 18

yes so far