1. 1

2. By MGMP Matematika SMPN
2 Sindang Indramayu

3. SOLIDS / bangun Ruang Standards 8, 10, 11
PYRAMID / Limas
PRISM / Prisma
CYLINDER / Tabung CONE kerucut SPHERE / Bola
3
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

4. 4

5. base STUDENT’S WORKSHEET
SURFACE AREA OF CYLINDER r
h
h
r
base
Fill in the blank !
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 =...............
5
7. The formula of surface area of Cylinder =....................................................

6. Let’s cek your answer
6

7. SURFACE AREA OF CYLINDERS
base r
r2
h 2 rh h
r
2 r
r2
base
r
Lateral/blanket (selimut) Area:
2 rh
Total Surface Area = Lateral Area + 2(Base Area)
T= 2 r h + 2 r 2
h= height
r= radius
7

8. Standards 8, 10, 11
VOLUME OF CYLINDERS
B= r2
V = Bh
V= r2 h
h
r
CYLINDER
8
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

9. Standards 8, 10, 11
Find the lateral area, the surface area and volume of a cylinder with a
radius of 20 cm and a height of 10 cm.
Total Surface Area = Lateral Area + 2(Base Area)
T= 2 rh + 2 r2
2
10 cm T=2 ( 20 cm)( 10 cm ) +2 ( 20 cm )
20 T= 400
2 2
cm + 2(400 cm )
cm
T = 400 cm 2
+ 800 Cm2
cm 2
Lateral Area: T = 1200
L =2 rh
Volume:
L=2 (20 cm )( 10 cm )
L=400 cm2 V= r2 h
2
V= ( 20 cm ) ( 10 cm )
2
V= (400 cm )(10 cm)
3
V= 4000 cm
9
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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.
Finding the radius: Lateral Area:
L =2 rh
C=2 r
L=2 (7 cm )(5 cm )
r= C
2 L= 70 cm2
Total Surface Area = Lateral Area + 2(Base Area)
14 T= 2 rh + 2 r2
r=
2 2
T = 2 ( 7 cm )( 5 cm ) + 2 ( 7 cm )
r=7 cm
T= 70 cm2 + 2(49 cm 2 )
T = 70 cm 2 + 98 cm 2
5 cm T = 168 cm 2
7 cm
10
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

11. Standards 8, 10, 11
Find the Volume for the cylinder below:
h
2
4
5
First we find the height:
Volume:
h 2 2 V= r2 h
5 = 4 + h2 2
V= ( 2) (3 )
25 = 16 + h2
-16 -16 V= ( 4 )(3)
4 5
h=9
2 V= 12 unit3
2
h= 9
h=3
11
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

12. Standards 8, 10, 11
2
The surface area of a right cylinder is 400 cm. If the height is 12 cm., find the
radius of the base.
We substitute values:
Total Surface Area:
Subtituting: -( 75.4 ) +
_ ( 75.4 )2 - 4(6.28 )(-400)
T= 2 r h + 2 r 2
2 400 = 2(3.14)r(12) + 2(3.14)r2 r=
T= 400 cm 2( 6.28 )
h= 12 cm 400 = 75.4 r + 6.28r 2
-400 -400 -75.4 +
_ 5685.16 + 10048
=3.14 r=
12.56
0 = 6.28r 2 + 75.4 r - 400
_
+
Using the Quadratic Formula: r = -75.4 15733.2
12.56
_
+
2 r = -75.4 125.43
-b +
_ b - 4ac 12.56
X= + -
2a
-75.4+125.43 -75.4 -125.43
2 r= r=
where: 0 = aX +bX +c 12.56
12.56
50.03 -200.83
r= r=
a= 6.28 12.56 12.56
From equation: b= 75.4 r 4 cm r -16
c= -400 12
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

13. Standards 8, 10, 11
SIMILARITY IN SOLIDS
Are this two cylinders similar?
4
6
8 3
4
= 8
6 3
These cylinders are NOT SIMILAR
13
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

14. Standards 8, 10, 11
The ratio of the radii of two similar cylinders is 2:5. If the volume of the
smaller cylinder is 40 units,3 what is the volume of the larger cylinder.
VOLUME 1 < VOLUME 2
Volume: VOLUME 1 VOLUME 2 2
V1 r1 h1
V= r2 h IF 2 2 THEN =
V1 = r1 h1 V2 = r2 h 2 V2 r2 h2
2
2
V1 2
r1 h1 V1 r1 h1 r1 h1
= AND = AND IF = = 2
V2 r2 h2
2 V2 r2 h2 They are similar r2 h2 5
Substituting values:
2
40 = 2 2 40 = 4 2 40 8
THEN =
V2 5 5 V2 25 5 V2 125
(40)(125) = 8V2
What can you conclude about the ratio of 8 8
the volumes and the ratio of the radii?
V2 = 625 units 3
14
PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

15. Practice diligently don’t be give up
Remember :
-Where there is will there is away
- You can if you think you can