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1 Standards 8, 10, 11 Classifying Solids PROBLEM 1 PROBLEM 2 Surface Area of Cylinders Volume of a Right Cylinder PROBLEM 3 PROBLEM 4 PROBLEM 5 PROBLEM 6 END SHOW PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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2 Standard 8: Students know, derive, and solve problems involving perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. Estándar 8: Los estudiantes saben, derivan, y resuelven problemas involucrando perímetros, circunferencia, área, volumen, área lateral, y superficie de área de figuras geométricas comunes. Standard 10: Students compute areas of polygons including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. Estándar 10: Los estudiantes calculan áreas de polígonos incluyendo rectángulos, triángulos escalenos, triángulos equiláteros, rombos, paralelogramos, y trapezoides. Standard 11: Students determine how changes in dimensions affect the perimeter, area, and volume of common geomegtric figures and solids. Estándar 11: Los estudiantes determinan cambios en dimensiones que afectan perímetro, área, y volumen de figuras geométricas comunes y sólidos. PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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3 PRISM PYRAMID CYLINDER SPHERE CONE Standards 8, 10, 11 SOLIDS PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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4 Standards 8, 10, 11 SURFACE AREA OF CYLINDERS h base h Lateral Area: 2 r L = h 2 r h r r r Total Surface Area = Lateral Area + 2(Base Area) T= 2 r h + 2 r 2 r 2 r 2 h= height r= radius 2 r PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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5 VOLUME OF CYLINDERS Standards 8, 10, 11 h r r 2 B= V = Bh V = r 2 h RIGHT CYLINDER PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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6 Find the lateral area, the surface area and volume of a right cylinder with a radius of 20 in and a height of 10 in. Standards 8, 10, 11 10 in 20 in Lateral Area: 2 r L = h L = 2 ( )( ) 10 in 20 in Total Surface Area = Lateral Area + 2(Base Area) T= 2 r h + 2 r 2 T = 2 ( )( ) + 2 ( ) 2 10 in 20 in T= 400 in + 2(400 in ) 2 2 L=400 in 2 T = 400 + 800 in 2 2 T = 1200 in 2 Volume: V = r 2 h ( ) 2 10 in 20 in V= (400 in )(10 in) 2 V= 4000 in 3 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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7 Standards 8, 10, 11 Find the lateral area and the surface area of a cylinder with a circumference of 14 cm. and a height of 5cm. C=2 r 2 2 r= C 2 2 r=7 cm Finding the radius: 14 5 cm 7 cm Lateral Area: 2 r L = h L = 2 ( )( ) 5 cm 7 cm L= 70 cm 2 Total Surface Area = Lateral Area + 2(Base Area) T= 2 r h + 2 r 2 T = 2 ( )( ) + 2 ( ) 2 5 cm 7 cm T= 70 cm + 2(49 cm ) 2 2 T = 70 + 98 cm 2 2 T = 168 cm 2 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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8 Standards 8, 10, 11 Find the Volume for the cylinder below: 2 5 First we find the height: 4 h h 4 5 5 = 4 + h 22 2 25 = 16 + h 2 -16 h = 9 2 2 h = 3 Volume: V = r 2 h ( ) 2 3 2 V= ( 4 )(3) V= 12 unit 3 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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9 Standards 8, 10, 11 The surface area of a right cylinder is 400 cm. If the height is 12 cm., find the radius of the base. Total Surface Area: T= 2 r h + 2 r 2 h= 12 cm Subtituting: 400 = 2(3.14)r(12) + 2(3.14)r 2 =3.14 400 = 75.4 r + 6.28r 2 -400 0 = 6.28r + 75.4 r - 400 2 We substitute values: 6.28 75.4 -400 + - X= -b b - 4ac 2a2a 2 +_ where:0 = aX +bX +c 2 = -( ) ( ) - 4( )( ) 2( ) 2 +_ r = -75.4 5685.16 + 10048 12.56 +_ r -75.4 15733.2 = 12.56 +_ r -75.4 125.43 = 12.56 +_ r -75.4+125.43 = 12.56 r 50.03 = r 4 cm r 12.56 -200.83 = r -16 r -75.4 -125.43 = 12.56 r Using the Quadratic Formula: a= 6.28 b= 75.4 c= -400 From equation: 2 T= 400 cm 2 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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10 6 3 SIMILARITY IN SOLIDS Standards 8, 10, 11 4 8 Are this two cylinders similar? These cylinders are NOT SIMILAR = 4 6 8 3 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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11 Standards 8, 10, 11 VOLUME 1 VOLUME 2 IF THEN AND r 1 r 2 = h 1 h 2 = 2 5 VOLUME 1 < VOLUME 2 V = r h 1 1 1 2 2 2 2 2 Volume: V = r 2 h V r h = 1 1 1 2 2 2 2 2 = 1 1 1 2 2 2 2 2 The ratio of the radii of two similar cylinders is 2:5. If the volume of the smaller cylinder is 40 units, what is the volume of the larger cylinder. 3 V 2 = 22 5 5 40 2 V 2 = 42 255 40 40 8 V 2 125 = (40)(125) = 8V 2 8 V = 625 units 2 3 = 1 1 1 2 2 2 V r h 2 Substituting values: THEN AND IF They are similar What can you conclude about the ratio of the volumes and the ratio of the radii? PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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12-3: Volumes of Prisms and Cylinders. V OLUME : the measurement of space within a solid figure Volume is measured in cubic units The volume of a prism.

12-3: Volumes of Prisms and Cylinders. V OLUME : the measurement of space within a solid figure Volume is measured in cubic units The volume of a prism.

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