Now that we know the shape of the cross section (image attached), we need to find a formula for its area. For any given height, h, write a formula to represent the area of the horizontal cross section of the cylinder with the cone removed by following these steps: Take the vertical cross section. Find the unknown dimension of the horizontal cross section using similarity of triangles. Use the given and determined dimensions to find the area of the horizontal cross section in terms of R and h. Now that you know a formula for the area of an arbitrary cross section of the inverted cone, you need to think about a cross section of the half sphere at the same height. If a horizontal plane cuts through the half sphere at a height of hunits, what shape will the cross section be?

Now that we know the shape of the cross section (image attached), we need to find a formula for its area. For any given height, h, write a formula to represent the area of the horizontal cross section of the cylinder with the cone removed by following these steps:

1. Take the vertical cross section.
2. Find the unknown dimension of the horizontal cross section using similarity of triangles.
3. Use the given and determined dimensions to find the area of the horizontal cross section in terms of R and h.
4. Now that you know a formula for the area of an arbitrary cross section of the inverted cone, you need to think about a cross section of the half sphere at the same height. If a horizontal plane cuts through the half sphere at a height of hunits, what shape will the cross section be?