1) The document discusses geometric solids such as prisms, pyramids, cylinders, cones, and spheres. It provides examples and formulas for calculating the surface areas and volumes of cylinders. 2) Worksheets are included that ask students to calculate the lateral area, surface area, and volume of cylinders given dimensions like radius and height. 3) Examples show how to set up and solve equations to find the radius of a cylinder given its surface area and height, or to find the height of a cylinder given a diagram.

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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
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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
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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
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8. Standards 8, 10, 11
VOLUME OF CYLINDERS
B= r2
V = Bh
V= r2 h
h
r
CYLINDER
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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
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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
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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
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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
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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
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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
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15. Practice diligently don’t be give up
Remember :
-Where there is will there is away
- You can if you think you can