Find the volume and surface area after rotating each figure around the \(y\)-axis.
1)
1)
2)
3)
4)
5)
6) Describe the solid formed when the given shape is revolved about the given line.
7) Sketch a shape that, when revolved about the \(y\)-axis, would result in the figure that would look like a donut called a torus.
8) Describe the solid formed when the triangle pictured is revolved about the line \(y = -x + 3\). Calculate the volume.
8) Describe the solid formed when the triangle pictured is revolved about the line \(y = -x + 3\). Calculate the volume.
9) Find the area of the cross section of a cube that passes through midpoints of three edges. The volume of the cube is \(216\) mm\(^3\)
10) Find the area of the cross section of the cube that has a volume of \(125\) cm\(^{3}\)?
11) Find the area of the cross section of the square pyramid that intersects a base edge and the midpoints of a lateral face.