Find the volume of the solid whose base is bounded by the circle x^2+y^2=4 with Equilateral triangle cross sections taken perpendicular to the x-axis.
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area of an equilateral triangle of side length " " is for your problem, the side of an equilateral cross-section is . equation for the volume of the described solid is get the cross-sectional area as a function of x and integrate.
I was able to work it out and got V=8. For semicircles, did i work it correctly? y=(4-x^2)^(1/2) A(x)=(pi r^2)/2 r=2(4-x^2)^(1/2) V= Integral pi((4-x^2)^2)dx Limits [-2,2]= 32pi/3
Originally Posted by HMV I was able to work it out and got V=8. not correct. how did you get V = 8? For semicircles, did i work it correctly? y=(4-x^2)^(1/2) A(x)=(pi r^2)/2 r=2(4-x^2)^(1/2) V= Integral pi((4-x^2)^2)dx Limits [-2,2]= 32pi/3 you got double the correct volume ... r = (4-x^2)^(1/2) note that it's much easier if you realized that it's just the volume of a hemisphere of radius 2 ... V = (2/3)pi*2^3 = 16pi/3 ok?
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