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Lesson 31 Surface Area and Volume of Pyramids Homework WS 7.3 Surface Area and Volume - Pyramids Surface Area Formula: SA = ½lp + B _________________________ Surface Area and Volume - Pyramids the shape of the base First thing to look for: _____________________________________ l height __________________ slant height __________________ (or altitude) side __________________ square pyramid __________________________________ Surface Area – Pyramid 1. Find the surface area of each regular pyramid with side length s, and slant height l. The number of sides of the base is given by n. s=6 l= 7 n=4 Square-lw SA = ½lp + B SA = ½lp + lw SA = ½(7)(24) + 36 SA = 84 + 36 SA = 120 Surface Area and Volume - Pyramids 2. Find the surface area with side length s and slant height l, with the number of sides of the base given by n. shape of the base First thing to look for?: _____________________________________ s =8 L = 9 n = 3 triangle __________________ SA = ½lp + B SA = ½lp + ½bh SA = ½(9)(24) + ½(8)(43) SA = 135.7 Surface Area and Volume - Pyramids The __________________of a solid is the total volume number of cubes that will exactly fill the interior. Volume Formula: V = ⅓Bh _________________________ area of the base Where B is:________________________ Volume – Pyramid shape of the base First thing to look for: _____________________________________ 7.6 3. V = ⅓Bh V = ⅓(12)(7.6) V = 30.4 m³ 3m 4m Surface Area and Volume - Pyramids 4. A pentagonal pyramid with a base area of 24 square units and a volume of 104 cubic units. What is the height? V = ⅓Bh 104 = ⅓(24)h 104 = 8h 13 = h Surface Area and Volume - Pyramid 5. Find the volume of a square pyramid with the given dimensions. Base edge of 4, and a height equal to the diagonal of the base V = ⅓Bh 42 4 V = ⅓(16)42 V = 30.2 4 Surface Area and Volume - Pyramid 6. A pyramid has a right triangle as its base, with leg lengths of 5 and 12. If the pyramids volume is 100, find its altitude. 12 5 V = ⅓Bh 100= ⅓(½(5)12)h 100= ⅓(30)h 100= 10h 10 = h Surface Area and Volume - Pyramids 7. Find the surface area of a pyramid with the given dimensions. shape of the base First thing to look for: _____________________________________ n = 3, s = 14, l = 14 SA = ½lp + B SA = ½(14)42 + ½(14)73 SA = 294 + 84.9 SA = 378.9 triangle __________________ 14 73 7 14 14