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1 Standards 8, 10, 11 Classifying Solids PROBLEM 1 PROBLEM 2 Surface Area of Cones Volume of a Right Cone PROBLEM 3 PROBLEM 4 PROBLEM 5 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 h r l l 2 r r 2 r L= area of sector 2 l area of sector area of circle perimeter of cone’s base perimeter of circle = 2 C= l 2 l = area of sector 2 r C= Area of Circle 2 l 2 r C= perimeter of cone’s base r 2 l l = area of sector 2 l 2 l TOTAL SURFACE AREA: T = area of sector + area of cone’s base 2 r B= area of sector l r =L= T = L + B T= 2 r l r + SURFACE AREA OF A RIGHT CIRCULAR CONE Standards 8, 10, 11 h= height r = radius l = slant height Lateral Area PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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5 h r VOLUME OF A RIGHT CIRCULAR CONE Standards 8, 10, 11 2 r B= V = Bh 1 3 V = 2 r 1 3 h h= height r = radius PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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6 Standards 8, 10, 11 Find the lateral area, the surface area and volume of a right cone with a height of 26 cm and a radius of 12 cm. Round your answers to the nearest tenth. h r =26 cm 12 cm = Lateral Area: l r L= we need to find the slant height, using the Pythagorean Theorem: l l = 26 + 12 2 2 2 l = 676 + 144 2 l = 820 2 l 28.6 cm Calculating the base area: 2 r B= 2 r 12 cm B= ( ) 2 B= 452.2 cm 2 Calculating surface area: T = L + B L= ( )( ) 12 cm 28.6 cm L = 1077.7 cm 2 T = 1077.7 cm + 452.2 cm 2 2 T = 1529.9 cm 2 Calculating the volume: 2 r V = 1 3 h 26 cm V = 1 3 ( ) 2 12 cm V = 3918.7 cm 3 B = 144 V = 1 3 ( ) 26 cm 144 cm 2 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 and volume of a right cone whose slant height is 9 ft and whose circumference at the base is 4 ft. Round your answers to the nearest tenth. h r l We need to find the radius: C=2 r 2 2 r= C 2 2 r= 2 ft 4 2 ft = we need to find the height, using the Pythagorean Theorem: 9 = h + 2 222 81 = h + 4 2 -4 h = 77 2 h = 8.8 ft Lateral Area: l r L= L= ( )( ) 2 ft 9.0 ft L = 56.5 ft 2 Calculating the base area: 2 r B= 2 ft B= ( ) 2 B= 12.6 ft 2 B = 4 Calculating surface area: T = L + B T = 56.5 ft + 12.6 ft 2 2 T = 69.1 ft 2 Calculating the volume: 2 r V = 1 3 h 8.8 ft V = 1 3 ( ) 2 2 ft V = 36.8 ft 3 V = 1 3 ( ) 8.8 ft 4 ft 2 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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8 Standards 8, 10, 11 Find the lateral area, the surface area, and the volume of a right cone whose height is 18 m and whose slant height is 22 m. Round your answers to the nearest unit. h = 18 m r l =22 m we need to find the radius, using the Pythagorean Theorem: 22 = r + 18 2 2 2 484= r + 324 2 -324 r = 160 2 r = 13 m Lateral Area: l r L= L= ( )( ) 13 m 22 m L = 898 m 2 Calculating the base area: 2 r B= 13 m B= ( ) 2 B= 531 m 2 B = 169 Calculating surface area: T = L + B T = 898 m + 531 m 2 2 T = 1429 m 2 Calculating the volume: 2 r V = 1 3 h 18 m V = 1 3 ( ) 2 13 m V = 3184 m 3 V = 1 3 ( ) 18m 169 m 2 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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9 Standards 8, 10, 11 Find the lateral surface of a cone whose volume is 900 mm and whose radius is 15 mm. Round your answers to the closest tenth. 3 2 r V = 1 3 h ( ) = 1 3 ( ) h 2 900 15 900 = 1 3 ( 225 ) h (3) 2700 = 225 h 225 225 h= 2700 706.5 h = 3.8 mm Now we draw the cone: h r 15= we need to find the slant height, using the Pythagorean Theorem: l = 3.8 + 15 2 2 2 l = 14.4 + 225 2 l = 239.4 2 l 15.5 mm Lateral Area: l r L= L= ( )( ) 15mm 15.5 mm L 730 mm 2 =3.8 Calculating the height: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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10 Standards 8, 10, 11 The ratio of the radii of two similar cones is 3:8. If the volume of the larger cone is 2090 units, what is the approximate volume of the smaller cone? 3 VOLUME 1 > VOLUME 2 2 r V = 1 3 h Volume: VOLUME 1 VOLUME 2 IF V = h 2 r 1 3 1 11 h 2 r 1 3 2 22 THEN V 1 h 2 r 1 3 11 V 2 h 2 r 1 3 22 = AND r 1 r 2 = h 1 h 2 = 8 3 V r h = 1 1 1 2 2 2 2 2 V 2 = 88 3 3 2090 2 V 2 = 648 93 2090 2090 512 V 2 27 = (27)(2090) = 512V 2 512 = 1 1 1 2 2 2 V r h 2 Substituting values: THEN AND IF They are similar V 110 units 2 3 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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Our learning goal is to be able to solve for perimeter, area and volume. Learning Goal Assignments 1.Perimeter and Area of Rectangles and Parallelograms.

Our learning goal is to be able to solve for perimeter, area and volume. Learning Goal Assignments 1.Perimeter and Area of Rectangles and Parallelograms.

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