12.1 Reteach - Classifying Solids

Tell whether each solid is a polyhedron. If it is, name the polyhedron.

• The solid is formed by polygons, so it is a polyhedron. The two bases are congruent triangles, so it is a triangular prism.

• The solid is not formed by polygons, so it is not a polyhedron.

• The solid is formed by polygons, so it is a polyhedron. The faces are all squares, so it is a cube.

• The solid is formed by curved surfaces, so it is a cylinder.

Tell whether each solid is a polyhedron. If it is, name the polyhedron. b. (Image of a cylinder)

• The cylinder has a curved surface, so it is not a polyhedron.

• The cylinder is a polyhedron called a prism.

• The cylinder is a polyhedron called a pyramid.

• The cylinder is a polyhedron called a cube.

In Exercises 1–3, tell whether the solid is a polyhedron. If it is, name the polyhedron. 1. (Image of a cube)

• Yes, it is a polyhedron. It is a cube.

• No, it is not a polyhedron. It is a sphere.

• No, it is not a polyhedron. It is a cylinder.

• Yes, it is a polyhedron. It is a pyramid.

In Exercises 1–3, tell whether the solid is a polyhedron. If it is, name the polyhedron. 2. (Image of a cone)

• No, it is not a polyhedron.

• Yes, it is a polyhedron called a prism.

• Yes, it is a polyhedron called a pyramid.

• Yes, it is a polyhedron called a cube.

In Exercises 1–3, tell whether the solid is a polyhedron. If it is, name the polyhedron. 3. (Image of a square pyramid)

• Yes, it is a polyhedron. It is a square pyramid.

• No, it is not a polyhedron. It is a cone.

• Yes, it is a polyhedron. It is a triangular prism.

• No, it is not a polyhedron. It is a cylinder.

In Exercises 4–6, describe the shape formed by the intersection of the plane and the solid. 4.

• The cross section is a circle.

• The cross section is a triangle.

• The cross section is a rectangle.

• The cross section is an ellipse.

In Exercises 4–6, describe the shape formed by the intersection of the plane and the solid. 5.

• The cross section is a triangle.

• The cross section is a circle.

• The cross section is a rectangle.

• The cross section is a hexagon.

In Exercises 4–6, describe the shape formed by the intersection of the plane and the solid. 6.

• The cross section is a rectangle.

• The cross section is a circle.

• The cross section is a triangle.

• The cross section is an ellipse.

What is the formula for the surface area S of a right prism with bases that are regular polygons? Fill in the blanks: S = 2B + L = ___ + ___, where B is the area of a base and L is the lateral area.

• aP + Ph

• 2B + Bh

• aP + 2h

• 2a + Ph

Find the surface area of the regular right prism shown in the diagram, where the height h is 10 inches, each side of the hexagonal base is 4 inches, and the perimeter P of the base is 24 inches. (Use the formula S = aP + Ph, where a ≈ 3.46)

• 240.24 square inches

• 221.6 square inches

• 208.8 square inches

• 192.4 square inches