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By MGMP Matematika SMPN 2 Sindang
Indramayu
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PRISM / Prisma PYRAMID / Limas
CYLINDER / Tabung SPHERE / BolaCONE kerucut
Standards 8, 10, 11SOLIDS / bangun Ruang
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
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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 !
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Let’s cek your answer
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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
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VOLUME OF CYLINDERSStandards 8, 10, 11
h
r
r 2B=
V = Bh
V = r 2 h
CYLINDER
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
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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
Total Surface Area = Lateral Area + 2(Base Area)
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
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
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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
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
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
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
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
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
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
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SIMILARITY IN SOLIDS
Standards 8, 10, 11
4
8
Are this two cylinders similar?
These cylinders are NOT SIMILAR
=4
683
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
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?
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved
Practice diligently don’t be give up
Remember : -Where there is will there is away
- You can if you think you can