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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Solids are usually divided into different types, all with different sets of characteristics. If each face of a solid is a polygon, the solid is called a *polyhedron*. A finer division can consist of types such as prism, pyramid, cylinder, cone, and sphere.

A prism is a three-dimensional object created by connecting a polygon with a translated version of the same polygon, vertex to vertex. All the faces are polygons, so prisms are polyhedra.

Pyramids are created by connecting a polygon's vertices with a single point, using line segments. Pyramids are also polyhedra.

A cylinder is made up of two congruent, parallel circles connected in a way corresponding to how the polygons in a prism are connected. As it contains circles, it is not a polyhedron.

Cones look like cylinders, though one of the circles is replaced by a point. Thus, they taper from a circle to a point. They are not polyhedra.

A sphere is the three-dimensional equivalent of a circle. It consists of every point in space at a certain distance away from the center of the sphere. It is not a polyhedron.

Name the solids and tell whether they are polyhedra.

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The first solid is made up of a circular base and top that are parallel, connected by a smooth surface. Thus, it is a cylinder, which is **not** a type of polyhedron.

The second solid's faces are six quadrilaterals and two hexagons, meaning six-sided polygons, on the left and right side. The two hexagons are parallel and connected vertex to vertex. This means that the second solid is a prism, which is a type of polyhedron. As the two parallel polygons are hexagons, the solid could be called a hexagonal prism.

The intersection between a plane and a solid is a two-dimensional surface called a cross-section. Often, it is possible to get different types of cross-sections from the same solid. For instance, the cross-section of a cylinder could be a rectangle or a circle, among other things.

Name the shapes of the cross-sections.

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The cross-section of the first solid has four vertices. As there are no parts of the solid that are curved, the cross-section can't have any curves either. Thus, the cross-section is in the shape of a quadrilateral.

This cross-section has three vertices instead. Similarly, the cube has no curved parts, meaning the cross-section has no curves. Therefore, the cross-section is a triangle.

A solid of revolution is a three-dimensional object formed by rotating some two-dimensional object around an axis. The axis is referred to as the *axis of revolution*. Rotating a rectangle with one side against the axis of revolution creates a cylinder.

Depending on the shape used, many different types of solids can be created.

Rotate

Sketch and describe the solid of revolution corresponding to the following shape and axis.

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Notice that if the top segment of the shape were extended to the left, the shape would be a triangle. Thus, we can think of it as a triangle without its pointy top. This means that the solid of revolution will be the same as though the shape were a triangle, but without the top. Thus, the resulting solid of revolution is a cone without a top.

It's base radius is $2$ units, top radius is $1$ unit, and its height is $3$ units.

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