Lesson 31 Surface Area and Volume of Pyramids Homework WS 7.3

SA = ½lp + B Surface Area and Volume - Pyramids Surface Area Formula: _________________________ SA = ½lp + B

the shape of the base l slant height height side square pyramid Surface Area and Volume - Pyramids the shape of the base First thing to look for: _____________________________________ l slant height height __________________ __________________ (or altitude) side __________________ square pyramid __________________________________

Square-lw SA = ½lp + B SA = ½lp + lw SA = ½(7)(24) + 36 SA = 84 + 36 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

shape of the base triangle SA = ½lp + B SA = ½lp + ½bh 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)(43) SA = 135.7

volume V = ⅓Bh area of the base Surface Area and Volume - Pyramids The __________________of a solid is the total number of cubes that will exactly fill the interior. Volume Formula: _________________________ V = ⅓Bh area of the base Where B is:________________________

shape of the base 3. V = ⅓Bh V = ⅓(12)(7.6) V = 30.4 m³ Volume – Pyramid shape of the base First thing to look for: _____________________________________ 3. V = ⅓Bh 7.6 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 V = ⅓(16)42 42 4 V = 30.2 4

V = ⅓Bh 100= ⅓(½(5)12)h 100= ⅓(30)h 100= 10h 10 = h 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. V = ⅓Bh 100= ⅓(½(5)12)h 100= ⅓(30)h 12 100= 10h 10 = h 5

shape of the base triangle SA = ½lp + B SA = ½(14)42 + ½(14)73 14 14 Surface Area and Volume - Pyramids 7. Find the surface area of a pyramid with the given dimensions. n = 3, s = 14, l = 14 shape of the base First thing to look for: _____________________________________ triangle __________________ SA = ½lp + B SA = ½(14)42 + ½(14)73 14 14 73 SA = 294 + 84.9 7 SA = 378.9 14