The document discusses the area and volume of cones. It defines key terms like cone, radius, height, slant height and explains the formulas to calculate the surface area and volume of a cone. The surface area of a cone is calculated as πr(s+r) where r is the radius and s is the slant height. The volume of a cone is calculated as 1/3πr^2h, where r is the radius and h is the height. Several examples are provided to demonstrate calculating the surface area and volume of cones using the given radii and heights.

1. What you will learn:
To state the area of a
cone side.
To calculate the area of
a cone side.
To state the volume of a
cone.
To calculate the volume
of a cone.
Key Terms:
•
•
•
•
•
Cone
Area of a cone side
Cone blanket
Volume of a cone
Height of a cone
What are you going to
learn?
to state the area of a
cone surface.
to calculate the area of
a cone surface.
to state the volume of a
cone.
to calculate the volume
of a cone.
Key Terms:
•
•
•
•
•
cone
area of a cone surface
cone blanket
volume of a cone
height of a cone
22..22
Surface Area of a Cone
LLook at the picture of a farmer cap below.
Figure 2.7
The farmer’s cap is cone in shape.
Figure 2.8 shows a cone and its parts.
A cone has two parts, namely the base
and the lateral.
s
t
Figure 2.8
On Figure 2.8 t is the height of the cone, r is the radius of the base, and s is the
slant height.
If the cone is cut along the slant s and its base, we will get the cone net which consists
of sector which has radius s and a circle with radius r, as shown by Figure 2.9.
38 / Student’s Book - Space Figures with Curved Surface

2. Base
Circumference
= 2πr
L = area of sector
(Lateral area)
s
A
B
Figure 2.9
Area of sector circumference of base
Area of circle circumference of big circle
=
Area of sector
s
r
π
π
2
2
=
The area of a cone surface
(L) equals the sum of the
area of the sector plus the
area of base. So the total
surface area is T = L + B
Area of sector =
s
rs2
π
Area of sector = π sr
Area of sector = π rs
T = L + B
T = π r (s + r)
with r = radius of cone and s=
slant height
Total
Surface
Area
Find the area of the following cone.
39 cm
14 cm
Mathematics for Junior High School Grade 9 / 39

3. Solution:
The radius of the base = ( r ) is 7 and the length of the slant height is 39, so
that
T = π r (r + s)
T =
7
22
7 (7 + 39)
T = 22 (46) = 1012
Therefore, the total area of the cone is 1.012 cm2.
Volume of a Cone
How do you find the volume of a cone?
Observe the following cones
Figure 2.10
The formula of the volume of a pyramid is V = 3
1
Bt. Because the cone base is a
circle with radius r, then B = π r 2 , so the volume of the cone is:
Volume of
a Cone
V = 3
1
Bh
V = 3
1
π r 2 t,
with r = radius of cone and
t = height of cone
40 / Student’s Book - Space Figures with Curved Surface

4. Work in pairs/groups
Instruments: Three (3) congruent cones made of plastic, a
cylinder whose height is the same as the height of the
cone, and sand.
* Fill all cones with sand until they are full. Pour the sand from
the cones into the cylinder. What will happen?
Mini - Lab
A certain cone has the radius of 3.5 cm, the height is 15 cm, and π =
7
22
.
Find the volume of the cone.
Solution:
The radius of the base r is 3.5 and the height is 15, so that
V = 3
1
π r 2 t
V =
3
1
.
7
22
. (3.5) 2 . 15
V = 11. (3.5). 5 = 192.5
So the volume of the cone is 192.5 cm3.
Mathematics for Junior High School Grade 9 / 41

5. A volume of a cone is 462 cm3, the height of the cone is 9 cm, and π
=
7
22
. Find the radius of the base.
A teacher assigns two of his students to make cones as tall as 10 cm. Ali
makes a cone with radius of 4 cm. Lia makes a cone with radius of 5 cm.
What is the volume of Ali’s cone? What is the volume of Lia’s cone?
1. Find the volume and the total surface area of each of the following cones. (π = 3.14)
a. b. c.
2. The radius of a cone base is 7 cm and the slant height is 13 cm.
Find :
a. the height of the cone
b. the volume of the cone
c. the total surface area
3. Mutia is going to have a birtdhday party. She will
make a party hat in conical figure as shown in the
picture on the left. If the height of the hat is 16 cm
and the radius is 12 cm, how wide is the paper
needed for one hat?
42 / Student’s Book - Space Figures with Curved Surface

6. 4. The volume of a cone is 1256 cm3. If the height of the cone is 12 cm, then find the
length of the cone radius (π = 3.14).
5. The base radius of a cone is 3.5 m, the volume of the cone is 115.5 m3, the value
of π =
7
22
. Find the height of the cone.
6. Critical Thinking A cone with a radius of 3 cm and a height
of 10 cm has the volume of 30π cm3.
a. What is the volume if the radius is twice as much as the
previous radius?
b. What is the volume of the cone now if the height is twice
as much as before?
c. What is the volume of the cone if the height and radius are
twice as much as before?
7. Find the radius (x ) of this cone if its volume is 21π.
Mathematics for Junior High School Grade 9 / 43