Thread: integral volume of equilateral triangle

can anyone help me with this problem?

The base of a certain solid is an equilateral triangle with altitude 12. Cross-sections perpendicular to the altitude are semicircles. Find the volume of the solid, using the formula

applied to the picture shown above (click for a better view), with the left vertex of the triangle at the origin and the given altitude along the -axis.

Thanks

Hello, davidude, and welcome to the forum.

I tried clicking, but I did not get any view at all If I understood it right, this is a semi-cone, and the x axis is the axis of the cone. Then all you need is to find the area of the cross-section at x and take an integral of it.