6 1 surf_area_vol_cylinders

By MGMP Matematika SMPN 2 Sindang

Indramayu

3

PRISM / Prisma PYRAMID / Limas

CYLINDER / Tabung SPHERE / BolaCONE kerucut

Standards 8, 10, 11SOLIDS / bangun Ruang

PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

5

STUDENT’S WORKSHEET

SURFACE AREA OF CYLINDER

h

base

base

h

r

r

r

1. Net of cylinder (jaring jaring tabung ) : ....................and ................

2. What’ shape (bentuk) Blanket (selimut) of cylinder ........................................?

3. The weight (lebar) of rectangle =..........................Cylinder (tabung)

4. The length (panjang ) of rectangle =...........................Of Circle ( lingkaran)

5. The formula of blanket (selimut) =.................................

6. The formula base of Cylinder =...............

7. The formula of surface area of Cylinder =....................................................

Fill in the blank !

6

Let’s cek your answer

7

SURFACE AREA OF CYLINDERS

h

base

base

h

Lateral/blanket (selimut) Area:

2 r 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

8

VOLUME OF CYLINDERSStandards 8, 10, 11

h

r

r 2B=

V = Bh

V = r 2 h

CYLINDER


9

Find the lateral area, the surface area and volume of a cylinder with a radius of 20 cm and a height of 10 cm.

Standards 8, 10, 11

10 cm20 cm

Lateral Area:

2 rL = h

L = 2 ( )( )10 cm20 cm


T= 2 rh + 2 r 2

T = 2 ( )( cm ) + 2 ( )2

10

20 cm 20 cm

T= 400 cm + 2(400 cm ) 2 2

L=400 cm2

T = 400 + 800cm 2 Cm 2

T = 1200 cm 2

Volume:

V = r 2 h

V = ( )2( )10 cm20 cm

V= (400 cm )(10 cm) 2

V= 4000 cm3


10

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

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


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


11

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


12

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


13

6

3

SIMILARITY IN SOLIDS

Standards 8, 10, 11

4

8

Are this two cylinders similar?

These cylinders are NOT SIMILAR

=4

683


14

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?


Practice diligently don’t be give up

Remember : -Where there is will there is away

- You can if you think you can

6 1 surf_area_vol_cylinders

Education

Transcript of 6 1 surf_area_vol_cylinders