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Geometric Solids

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Use the following key for the formulas in this presentation. b = based = diameter h = heightr = radius l = lengthpi = 3.14 w = width l = slant height

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Cylinder The cylinder has two circular bases. h r

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Cylinder Volume = (pi)r 2 h h r

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Cylinder SA = 2(pi)rh +2(pi)r 2 h r

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Cone The cone consist of one circular base. l h r

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Cone Volume = 1/3(pi)r 2 h l h r

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Cone SA = (pi)rl + (pi)r 2 l h r

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Sphere r V = (4/3)(pi)r 3

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Sphere r SA = 4(pi)r 2

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Rectangular Prism The Rectangular Prism has two rectangular bases. w h l

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Rectangular Prism V = lwh w h l

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Rectangular Prism SA = 2(lw + hw + lh) w h l

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Square Pyramid The Square Pryamid has one square base. l l h w

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Square Pyramid V = (1/3)lwh l l h w

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Square Pyramid SA = 2ll + l 2 l l h w

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Example Problems

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Find the volume of the cylinder. 10 in 6 in

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Find the volume of the cylinder. V = (pi) r 2 h 10 in 6 in

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Find the volume of the cylinder. V = (pi) r 2 h pi = 3.14 r = 6 h = 10 10 in 6 in

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Find the volume of the cylinder. V = (pi) r 2 h pi = 3.14 r = 6 h = 10 V = (3.14)(6 2 )(10) 10 in 6 in

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Find the volume of the cylinder. V = (pi) r 2 h pi = 3.14 r = 6 h = 10 V = (3.14)(6 2 )(10) V = 1130.4 in 3 10 in 6 in

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Find the surface area of the sphere. 14 cm

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Find the surface area of the sphere. SA = 4 (pi) r 2 14 cm

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Find the surface area of the sphere. SA = 4 (pi) r 2 pi = 3.14 diameter = 14 so… r = 7 14 cm

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Find the surface area of the sphere. SA = 4 (pi) r 2 pi = 3.14 diameter = 14 so… r = 7 SA = 4(3.14)(7 2 ) 14 cm

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Find the surface area of the sphere. SA = 4 (pi) r 2 pi = 3.14 diameter = 14 so… r = 7 SA = 4(3.14)(7 2 ) SA = 615.4 cm 2 14 cm

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Find the volume of the prism. 1 ft 4 in 8 in

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Find the volume of the prism. V = lwh 1 ft 4 in 8 in

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Find the volume of the prism. V = lwh l = 8 in w = 4 in h = 1 ft = 12 in 1 ft 4 in 8 in

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Find the volume of the prism. V = lwh l = 8 in w = 4 in h = 1 ft = 12 in V = (8)(4)(12) 1 ft 4 in 8 in

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Find the volume of the prism. V = lwh l = 8 in w = 4 in h = 1 ft = 12 in V = (8)(4)(12) V = 384 in 3 1 ft 4 in 8 in

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r=8 in r= 1 ft r= 1.8 ft How much snow did it take to make the snowman?

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r=8 in r= 1 ft r= 1.8 ft How much snow did it take to make the snowman? Volume of top: (4/3)(3.14)(.7 3 ) = 1.4 ft 3

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r=8 in r= 1 ft r= 1.8 ft How much snow did it take to make the snowman? Volume of middle: (4/3)(3.14)(1 3 ) = 4.2 ft 3

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r=8 in r= 1 ft r= 1.8 ft How much snow did it take to make the snowman? Volume of bottom: (4/3)(3.14)(1.8 3 ) = 24.4 ft 3

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r=8 in r= 1 ft r= 1.8 ft How much snow did it take to make the snowman? Total Volume: 1.4 + 4.2 + 24.4 = 30 ft 3

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Created by: Lisa Alcott Lisa_Alcott@pinellas.k12kfl.us

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