PRE-ALGEBRA

Surface Area: Pyramids, Cones, and Spheres (10-6) How can you find the surface area of a pyramid using a formula? Surface Area (S.A.) of a Pyramis Formula S.A. ( pyramid ) = L.A. + B where the L.A. (lateral area) = ½ · perimer of base · slant height (L.A. = ½pl) and B is the area of the Base

PRE-ALGEBRA Surface Area: Pyramids, Cones, and Spheres (10-6) Example: Find the surface area of the following pyramid. Method 1: Formula Method Step 1: Find the lateral area. L.A. = ½pl (½ · perimeter of base · slant height) = ½ ( )(16) = ½ (48) (16) = ½ (768) = 384 Step 2: Find the surface area. S.A. = lateral area (L.A.) + area of base (B) = = = 528 Method 2: Net Method Add the areas of the base and the triangles that make the pyramid Area of triangular face = ½bh (½ · base · height) = ½(12)(16) = 96 Area of base = lw (length · width) = 12 2 = 144 Area of base + area of each face = (4) = = 528 The surface area of the square pyramid is 528 square cm. (cm. 2 )

PRE-ALGEBRA Find the surface area of the square pyramid. The surface area of the pyramid is 105 m 2. Step 1 L.A. = p Use the formula for lateral area = 20 8 = 80 p = 4(5) and = Step 2 S.A. = L.A. + B Use the formula for surface area. = Lateral area = 80 and B = 5 2. = = 105 Surface Area: Pyramids Cones and Spheres LESSON 10-6 Additional Examples

PRE-ALGEBRA Surface Area: Pyramids, Cones, and Spheres (10-6) How can you find the surface area of a cone using a formula? Surface Area (S.A.) of a Cone Formula S.A. ( cone ) = L.A. + B where the L.A. (lateral area) = ½ · perimer of base · slant height (L.A. = ½pl) and B is the area of the Base

PRE-ALGEBRA Surface Area: Pyramids, Cones, and Spheres (10-6) Example: Find the surface area of the following cone. Method 1: Formula Method Step 1: Find the lateral area. L.A. =  rl (  · radius of base · slant height) =  (4)(10) = ½(768) = 40  Step 2: Find the surface area. S.A. = lateral area (L.A.) + area of base (B) = 40  +  r 2 = 40  +  (4) 2 = 40  + 16  = 56   16 (3.14)  176 Method 2: Net Method Add the areas of the base and the cone itself Area of cone face = ½Ch (½ · Circumference of bottom · height) = ½(2  r)h = ½(2)(  )(4)(10) = 40  Area of base =  r 2 =  (4) 2 = 16  Area of base + area of the face = 16  = 40  = 56   16 (3.14)  176 The surface area of the cone is 56  square cm. (cm. 2 ) or about 176 square cm. (cm. 2 )

PRE-ALGEBRA Find the surface area of the cone. The surface area of the cone is about 94 m 2. Step 2 S.A. = L.A. + B Use the formula for surface area. 21  +  (3) 2 L.A. = 21  and B =  (3) 2. = 30 = 94.2 Use 3.14 for. Surface Area: Pyramids Cones and Spheres LESSON 10-6 Additional Examples Step 1 L.A. = r Use the formula for lateral area.  (3)(7) r = 3 and = 7. = 21 

PRE-ALGEBRA Surface Area: Pyramids, Cones, and Spheres (10-6) How can you find the surface area of a sphere using a formula? Surface Area (S.A.) of a Sphere Formula S.A. ( sphere ) =.4  r 2 Example: Find the surface area of the following basketball. S.A.(sphere) = 4  r 2 (4  · radius 2 ) r = ½ diameter = ½ (10) = 5 = 4  (5) 2 = 4  (25) = 100   100 (3.14)  314 The surface area of the sphere is 100  square in. (in. 2 ) or about 314 square in. (in. 2 )

PRE-ALGEBRA Earth has an average radius of 3,963 mi. What is Earth’s approximate surface area to the nearest 1,000 mi 2 ? Assume that Earth is a sphere. The surface area of Earth is about 197,259,000 mi 2. S.A. = 4 r 2 Use the formula for surface area.  197,259,435 = 62,821,476 = 4 (3,963) 2 r  3,963 (“average” is not an exact number) Surface Area: Pyramids Cones and Spheres LESSON 10-6 Additional Examples

PRE-ALGEBRA Find the surface area of each space figure. Round to the nearest whole unit. 1.a square pyramid with base edge 80 m and slant height 100 m 2.a cone with slant height 22 cm and radius 7 cm 3.a sphere with radius 12 cm about 1,809 cm 2 22,400 m 2 about 637 cm 2 Surface Area: Pyramids Cones and Spheres LESSON 10-6 Lesson Quiz