Find the volume of the solid whose base is enclosed by the circle....?

Question

Find the volume of the solid whose base is enclosed by the circle
x^2 + y^2 = 100 and whose cross sections taken perpendicular to the x-axis are equilateral triangles.

ACK! Any help with this is greatly appreciated ><

Answer 1

Integration: you have a row of triangles starting with side 0, going up to size 10, and then back down to 0. The area of an equilateral triangle with side s is s^2sqrt(3)/4, so the "volume" of each slice is s^2sqrt(3)/4dy.

What is s? It is 2 times the x coordinate of the circle,
r = 2sqrt(100 - y^2)

So the answer is integral from -10 to 10 of (100 - y^2)sqrt(3)dy

Answer 2

x^2+y^2=4 is the equation of a circle with radius 2 or diameter of four when you consider that go section is sq., the top is an same as diameter i.e. 4 quantity is pi*r^2*top pi*4*4 16pi