A plane that is to the base of the figure will create a cross section that is the same shape as the base.

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1 Objective: Notes: Surface Area of Solids Name Cross Sections: A cuts through a solid figure to create a cross section. Depending on the way in which the plane cuts through the figure will determine the of the cross section. A plane that is to the base of the figure will create a cross section that is the same shape as the base. A plane that cuts to the base of the figure will create a different cross sections shape. Lateral and Surface Area of Prisms A is a polyhedron with exactly two congruent, parallel faces, called. Other faces are. You name a prism by the shape of its bases. An of a prism is a perpendicular segment that joins the planes of the bases. (h) of the prism is the length of an altitude. A prism may either be right or oblique. **You may assume that a prism is a right prism unless stated or pictured otherwise!**

2 of a prism is the sum of the areas of the lateral faces. is the sum of the lateral area and the area of the two bases. Lateral and Surface Areas of a Prism lateral area of a right prism is the product of the perimeter of the base and the height. L.A. = surface area of a right prism is the sum of the lateral area and the areas of the two bases. S.A. = Example 1: Use formulas to find the lateral area and surface area of the prism. 4 cm 3 cm 6 cm Example 2: Use formulas to find the lateral area and surface area of the regular hexagonal prism. 12 m Lateral and Surface Area of Cylinders Like a prism, a has two congruent parallel. However, the bases of a cylinder are. 6 m An of a cylinder is a perpendicular segment that joins the planes of the bases. (h) of a cylinder is the length of an altitude. **You may assume that a cylinder is a right cylinder unless stated or pictured otherwise.**

3 To find the area of the curved surface of a cylinder, visualize unrolling it. area of the resulting rectangle is the of the cylinder. of a cylinder is the sum of the lateral area and the areas of the two circular bases. Lateral and Surface Areas of a Cylinder lateral area of a right cylinder is the product of the circumference of the bases and the height of the cylinder. L.A. = surface area of a right cylinder is the sum of the lateral area and the areas of the two bases. S.A. = Example 3: radius of the base of a cylinder is 4 in. and its height is 6 in. Find the surface area of the cylinder in terms of π. Example 4: Find the surface area of a cylinder with height 10 cm and radius 10 cm in terms of π. Lateral and Surface Area of Pyramids A is a polyhedron in which one face (the ) can be any polygon and the other faces (the ) are triangles that meet at a common point (called the of the pyramid). You can name a pyramid by the shape of its base. of a pyramid is the perpendicular segment form the vertex to the plane of the base. length of the altitude is the (h) of the pyramid.

4 A regular pyramid is a pyramid whose base is a polygon and whose lateral faces are triangles. ( l ) is the length of the altitude of a lateral face of the pyramid. **You can assume that a pyramid is regular unless stated otherwise.** of a pyramid is the sum of the areas of the congruent lateral faces. To find the of a pyramid, add the area of its base to its lateral area. Lateral and Surface Areas of a Regular Pyramid lateral area of a regular pyramid is half the product of the perimeter of its base and the slant height. LA = surface area of a regular pyramid is the sum of the lateral area and the area of the base. SA = Example 5: Find the surface area of the hexagonal pyramid with slant height of 9 in. a side Length of 6 in. and a base apothem of 3 3in. 9 in 3 3 in 6 in Sometimes the slant height of a pyramid is not given. You must calculate it before you can find the lateral or surface area. Example 6: Social Studies Great Pyramid at Giza, Egypt was built about 2580 B.C. as a final resting place for Pharaoh Khufu. At the time it was built, its height was about 481 ft. Each edge of the square base was about 756 ft long. What was the lateral area of the Great Pyramid? What is the surface area to the nearest square foot?

5 Lateral and Surface are of Cones A is pointed like a pyramid, but its is a circle. In a right cone, the is a perpendicular segment from the to the center of the base. ( h ) is the length of the altitude. ( l ) is the distance from the vertex to a point on the edge of the base. As with a pyramid, the is ½ the perimeter (circumference) of the base times the slant height. formulas for the lateral area and of a cone are similar to those for a pyramid. **You can assume that a cone is a right cone unless stated or pictured otherwise.** Lateral and Surface Areas of a Cone lateral area of a right cone is half the product of the circumference of the base and the slant height. LA = surface area of a right cone is the sum of the lateral area and the area of the base. SA = Example 7: Find the surface area of the cone in terms of π. 25 cm 15 cm Example 8: Chemistry funnel is in the shape of a cone. How much filter paper do you need to line the funnel? 8 cm 7.5 cm