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The base of a solid is the circle x2 + y2 = 9. Cross sections of the solid perpendicular to the x-axis are equilateral triangle...Asked by Alice
The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid?
36√3
36
18√3
18
36√3
36
18√3
18
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Answered by
Anonymous
So the cross sections (parallel to the base) are also circles, of formula
x^2+y^2=r^2, where r is radius.
Now given the vertical cross sections are equilaterial, that means the sides at x or y at zero, is equal to twice the radius of the base, or 6.
so the height of the solid is 6/sqrt3 (sketch a equilateral triangle of side 6), or h=2.44
at this point, you dont need calculus and integration (you can do that), but knowing the volume of a cone is 1/3 base area * height, or
volume= 1/2 (PI*3^2)(2.44)
x^2+y^2=r^2, where r is radius.
Now given the vertical cross sections are equilaterial, that means the sides at x or y at zero, is equal to twice the radius of the base, or 6.
so the height of the solid is 6/sqrt3 (sketch a equilateral triangle of side 6), or h=2.44
at this point, you dont need calculus and integration (you can do that), but knowing the volume of a cone is 1/3 base area * height, or
volume= 1/2 (PI*3^2)(2.44)
Answered by
jugfydrytui
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