Obj. 52 Pyramids and Cones

• 1. Obj. 52 Pyramids and Cones The student is able to (I can): Find the volume and lateral and total surface areas of pyramids and cones.

2. Volume The volume of a pyramid with base area B and height h is 1 V Bh 3 = The volume of a cone is 21 1 V Bh r h 3 3 = = 3. Examples Find the volume of the following: 1. 2. 2 22 3 B 3 yd 4 = = = = 31 V ( 3)(3) 3 yd 3 10 mm 10 mm 13 mm 5 mm 12 mm (Pyth. triple) 21 V (10 )(12) 3 = 3 400 mm= 2 yd 3 yd 2 yd 4. Examples 3. 4. 7 ft. 21 ft. 2 31 V (7 )(21) 343 ft 3 = = 25 mi 20 mi 21 V (10 )(25) 3 = 32500 mi 3 = 5. Surface Area To find the lateral area of the pyramid, find the area of each of the faces. Perimeter of base slant height ( ) 1 L P 2 = For the total surface area, add the area of the base. S = L + B 6. Likewise, for a cone, the lateral area is ( ) 1 L 2 r r 2 = = and the total surface area is 2 S L r= + 7. Examples Find the lateral and surface area of the following: 1. 2. 8 in. 20 in. 5 m 5 m 2 8 3 B 6 4 = 2 96 3 in= 1 L [(6)(8)](20) 2 = 2 480 in= 2 S 480 96 3 in= + 2 646.3 in 5 2 m L (5)(5 2)= 2 25 2 m= 2 S 25 2 25 m= + 2 189.6 m