Download 9.1-3 Notes: Surface Area of Solids Name__________________

9.1‐3 Notes: Surface Area of Solids Name__________________ Objective: 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. The (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!** The of a prism is the sum of the areas of the lateral faces. The is the sum of the lateral area and the area of the two bases. Lateral and Surface Areas of a Prism The lateral area of a right prism is the product of the perimeter of the base and the height. L.A. = The 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 6 m Lateral and Surface Area of Cylinders Like a prism, a _______________ has two congruent parallel ____________ . However, the bases of a cylinder are ___________. An ________________ of a cylinder is a perpendicular segment that joins the planes of the bases. The _______________ (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.** To find the area of the curved surface of a cylinder, visualize “unrolling” it. The area of the resulting rectangle is the______________ ______ of the cylinder. The_____________ _________ 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 The lateral area of a right cylinder is the product of the circumference of the bases and the height of the cylinder. L.A. = The surface area of a right cylinder is the sum of the lateral area and the areas of the two bases. S.A. = Example 3: The 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. The_____________ of a pyramid is the perpendicular segment form the vertex to the plane of the base. The length of the altitude is the ____________ (h) of the pyramid. A regular pyramid is a pyramid whose base is a ____________ polygon and whose lateral faces are ______________ triangles. The ( 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.** The _________________ _________ 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 The lateral area of a regular pyramid is half the product of the perimeter of its base and the slant height. LA = The 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 The 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? 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. The ___________( h ) is the length of the altitude. The ( 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. The 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 The lateral area of a right cone is half the product of the circumference of the base and the slant height. LA = The 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 The funnel is in the shape of a cone. How much filter paper do you need to line the funnel? 8 cm 7.5 cm