1 standards 8, 10, 11 classifying solids problem 1 problem 2 surface area of cylinders volume of a...

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

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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.

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3

PRISM PYRAMID

CYLINDER SPHERECONE

Standards 8, 10, 11SOLIDS

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4

Standards 8, 10, 11SURFACE AREA OF CYLINDERS

h

base

base

h

Lateral Area:

2 rL = h

2 rh

r

r

r

Total Surface Area = Lateral Area + 2(Base Area)

T= 2 rh + 2 r 2

r 2

r 2

h= heightr= radius

2 r

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5

VOLUME OF CYLINDERSStandards 8, 10, 11

h

r

r 2B=

V = Bh

V = r 2 h

RIGHT CYLINDER

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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 in20 in

Lateral Area:

2 rL = h

L = 2 ( )( )10 in20 in

Total Surface Area = Lateral Area + 2(Base Area)

T= 2 rh + 2 r 2

T = 2 ( )( ) + 2 ( )210 in20 in 20 in

T= 400 in + 2(400 in )2 2

L=400 in2

T = 400 + 800in2 in2

T = 1200 in2

Volume:

V = r 2 h

V = ( )2( )10 in20 in

V= (400 in )(10 in) 2

V= 4000 in3

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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 r22

r= C2

r=2

r=7 cm

Finding the radius:

14

5 cm 7 cm

Lateral Area:

2 rL = h

L = 2 ( )( )5 cm7 cm

L= 70 cm 2

Total Surface Area = Lateral Area + 2(Base Area)

T= 2 rh + 2 r 2

T = 2 ( )( ) + 2 ( )25 cm7 cm 7 cm

T= 70 cm + 2(49 cm )22

T = 70 + 98 cm 2cm 2

T = 168 cm2

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8

Standards 8, 10, 11Find the Volume for the cylinder below:

25

First we find the height:

4

h

h

4 5

5 = 4 + h2 2 2

25 = 16 + h2

-16 -16

h = 92

h = 92

h = 3

Volume:

V = r 2 h

V = ( )2( )32

V= ( 4 )(3)

V= 12 unit3

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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 rh + 2 r 2

h= 12 cm

Subtituting:

400 = 2(3.14)r(12) + 2(3.14)r2

=3.14

400 = 75.4 r + 6.28r2

-400 -400

0 = 6.28r + 75.4 r - 4002

We substitute values:

6.28

6.2875.4 75.4 -400

+ -X=-b b - 4ac

2a

2+_

where: 0 = aX +bX +c2

=-( ) ( ) - 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 =

12.56r

12.5650.03

=r

4 cmr

12.56-200.83

=r

-16r

-75.4 -125.43 =

12.56r

Using the Quadratic Formula:

a= 6.28b= 75.4c= -400

From equation:

2

T= 400 cm2

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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

683

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11

Standards 8, 10, 11

VOLUME 1 VOLUME 2IF THEN

AND r 1

r 2

=h1

h2

= 25

VOLUME 1 < VOLUME 2

V = r h 1 1 1

2 V = r h 2 2 22

Volume:

V = r 2 h

V r h

V r h=

1 1 1

2 2 2

2

2

=1 1 1

2 2 2

V r h

V r h

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

V2

=2 25 5

402

V2

=4 2

25 540 40 8

V2 125=

(40)(125) = 8V2

8 8

V = 625 units23

=1 1 1

2 2 2

V r h

V r h

2

Substituting values:

THEN

AND IFThey are similar

What can you conclude about the ratio of the volumes and the ratio of the radii?

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