1. Figure 2.3
Figure 2.2
Figure 2.1
Figure 2.4
22..11
Total Surface Area
What are you going to
learn?
to mention the elements
of a cylinder.
to draw cylinder nets.
to explain the formula of
the area of a cylinder’s
surface.
to calculate the area of
a cylinder’s surface.
to explain the formula of
the volume of a cylinder.
to calculate the volume
of a cylinder.
to calculate the height or
radius of a cylinder if the
volume is given.
Key Terms:
Observe the pictures of
some cans on the right .
What are the shapes of the
cans?
A cylinder has two circular
bases and a lateral face.
• cylinder
• area of a cylinder’s
surface
• area of a cylinder’s base
• volume of a c
Here are the mathematical figures.
ylinder
A
B
A
B
If we cut the cylinder along the bases and along
straight line AB in Figure 2.3 and we spread it on
a plane, we will get a net as in Figure 2.4.
Mathematics for Junior High School Grade 9 / 33

2. For a better understanding, take a can
of milk or any can with a label. If you
cut the label as in Figure 2.5 and
spread it on a plane, you will get a
rectangular figure. The width of the
rectangle is equal to the the height of
the can and the length is the
circumference of the base.
Figure 2.5
Now, how do we find the total surface area?
Look at the net of the cylinder below. The total surface area can be
found by adding all the three areas.
Total surface area = lateral area + 2 base area
= 2πrh + 2πr2
If the total surface area is called T, we have the formula
for T:
Area of top
base = πr2
Area of bottom
base = πr2
Area of lateral face
= 2πrh
Remember
π is a number
indicating the
comparison
between a round of
one circle (say K)
with its diameter
(say d)
π=
d
K
The approximate
value of π is 7
22 or
3.14.
T = 2πrh + 2πr2
,
where r = radius of cylinder
h = height
Formula for
the Total
Surface Area
34/ Student’s Book – Space Figures with Curved Surface

3. Find the smallest area of an alluminum sheet for
making a can like the picture below. (Use π =
7
22 )
7 cm
11.5 cm
Volume of a Cylinder
What is the volume of a cylinder? We can use the formula of the volume
of a prism.
(a) (b) (c)
Figure 2.6
The volumes of regular prisms (a) and (b) are the base area (A) times the
height (h). If the number of the sides increases to infinity, then the base
will be a circle. So, the volume of the cylinder is:
V = A × h
V = (π r2 ) × h
V = π r2
h,
with r = radius of cylinder
h = height of cylinder
Formula for the
Volume of a
Cylinder
Mathematics for Junior High School Grade 9 / 35

4. Real life Situation
In many birthday parties, we often serve a
birthday cake like the picture the on the left.
Mostly, the cake of this kind is circular in
shape. The diameter of the cake is 10 cm and
the height is 5 cm. Find the volume of the
cake.
To celebrate his birthday Arry serves her
guests a two-layer cake as seen on the
picture on the left. The height of each layer is
7 cm.
If the diameter of the bottom cake is 30 cm
and the diamater of the top one is 25 cm, find
the difference in volume of both layers.
1. Determine the total surface area and the volume of each of the following
cylinders.
a) b) c)
7 cm
10 cm
15 cm
14 cm
7 cm
12 cm
36/ Student’s Book – Space Figures with Curved Surface

5. 2. The front side of a heavy machine is a cylindrical in
shape. The diameter of this part is 6 feet (foot/feet =
feet contracted into ft) and the length is 8 feet. How
wide is the surface of the cylinder? What is the
volume of the cylinder?
3. Someone wants to make a cylinder with the volume of 600 cm3. If the
radius of the base of the cylinder is 5 cm, what is the height of the cylinder?
4. If the volume of a cylinder is 135 π cm3 and the height is 15 cm, what is the
radius of the cylinder?
5. An oil refinery whose height is 32 m and whose diameter of the base side is 84 m
will be painted. What is the area of the refinery to be
painted? If one gallon of paint can be used to paint an
area of 325 m3, how many gallons of paint are
required?
6. The radius of a cylindrical tank is enlarged so that its radius is twice larger
than before. Find how much larger is its volume after being enlarged.
7. The surface of a swimming pool has a circle in shape with circumference of
77 meters. Calculate how much water is needed to fill in the pool if the
height is 1.2 meters.
Mathematics for Junior High School Grade 9 / 37