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[Music] foreign [Music] [Applause] [Music] x squared plus y squared equals 64 which is a circle with Center at the origin radius eight and if we wanted to solve for y it would look like this right here and so the top half of that Circle is y equals the positive square root of 64 minus x squared and the bottom of that Circle or this semicircle is y equals to negative square root of 64 minus x squared so for each X between negative 8 and 8 this distance right here which is the base of an equilateral triangle is this y-coordinate minus this y coordinate which gives us two of those Y coordinates that what thats what this s is right here the side of an equilateral triangle and the area of an equilateral triangle is s squared radical three over four so if we pick this is this is the kind of what were picturing as one of the Cross sections that are perpendicular to the x-axis were kind of visualizing this equilateral triangle coming up out of the ground and you can see whoop that if I go