This document discusses the area and volume of spheres. It provides the formulas for calculating the surface area and volume of a sphere. The surface area formula is A = 4πr^2 and the volume formula is V = (4/3)πr^3, where r is the radius of the sphere. It also gives examples of using these formulas to calculate the area and volume of various spheres.

1. 22..33
Area of a SphereWhat are you going to
learn?
to state the area of a
sphere.
to calculate the area
of a sphere.
to state the volume of
a sphere.
to calculate the
volume of a sphere.
Key Terms
any kinds of fruits have sphere-like shapes, such as
oranges, tomato, melons.
MM
Figure 2.11
:
• sphere
• area of a sphere.
• volume of a sphere.
Mention other objects around you, which are spheres in shape. A volley ball and a
basket ball are spheres in shape.
Figure 2.12
How do you find the surface area of a ball? Do these activities.
/ Student’s Book – Space Figures with Curved Surface44

2. Work in Groups.
Instrument and material : a slice of a hemispherical plastic ball, a nail
and a piece of string.
Mini - Lab
How to do it :
Make a hemispherical slice of a ball and stick the nail at the centre of the
surface like the following pictures.
(a) (b)
Arrange the string as Figure (a) till it covers the entire surface. Measure that
the length of the string, say the length is x. Next, arrange the string on the
hemispherical surface of the ball till it covers the entire surface, as shown in
Figure (b). Measure the string length needed, say y.
Compare the lengths of strings y and x. Is it true that the ratio is y : x = 2 : 1?
or the ratio of y and x approaches 2:1? If the ratio only approaches 2:1, then
round it off to the nearest integer, so that y : x = 2:1.
Stated in an equation, y = 2x. To cover the whole surface of the ball, we need
2y strings, so that the area of the sphere surface (L) is formulated as
A = 2y = 2. 2x = 4x.
Because x equals the area of a circle, then x = π r 2. So the area of a sphere
(L) is
A = 4 π r 2,
with r = radius of a sphere
Formula for
the Surface of
Sphere
Mathematics for Junior High School Grade 9 / 45

3. A solid spherical object has a diametre of 4.2 cm. Find the surface area of the
object (π =
7
22
).
Solution :
The radius of the solid spherical object r is 2.1, so that the surface area of
the object
A = 4π r 2
A = 4
7
22
(2.1) 2
A = 55.44
So the surface area of the object is 55.44 cm2.
What is the radius of the sphere when its area is 78
7
4
cm2 and π =
7
22
?
/ Student’s Book – Space Figures with Curved Surface46

4. Volume of Sphere
How do you find the volume of a sphere?
Mini - LabMini - Lab
Look at Figure 1 which shows a hemispherical object with a
radius of r and Figure 2 which shows a cone with a length of r and a
height of t. If this cone is filled entirely with water and then it is poured
into the hemispherical object, then the hemispherical object can
accomodate precisely twice the volume of the cone. Try to do it.
Figure (1). Figure (2).
Volume of a hemispherical object = 2 × volume of a cone
Volume of a sphere = 2 × 2 volume of a cone
= 4 × volume of a cone
= 4 ×
3
1
π r 2
t
=
3
4
π r 2
.r, t = r.
=
3
4
π r 3
r
r
t= r
So the formula of the Volume of a sphere (V) is
V = 3
4 πr3
,
With r = radius of sphere
Formula for the
Volume of a
Sphere
Mathematics for Junior High School Grade 9 / 47

5. Find the volume of a sphere with a radius of 10 cm and π = 3.14.
Solution
The radius of the sphere r is 10, so the volume of the sphere
V =
3
4 π r 3
V =
3
4 3.14 (10)3
V =
3
4 (3140) = 4186
3
2
So the volume of the sphere is 4,186
3
2
cm3.
The radius of a sphere is 3 cm. Find the volume and the surface area.
Solution:
V =
3
4
π r 3
=
3
4
π × 3 3 =
3
4
π × 3 × 3 × 3
= 36 π
L = 4 π r2
= 4π × 3 × 3 = 36π
So the volume is 36π cm3 and the surface area is 36π cm2
Find the length of the radius of a sphere, in which the volume is 1.437 3
1
cm3 and
π =
7
22
.
/ Student’s Book – Space Figures with Curved Surface48

6. 1. Find the volume and the area of each of the following spheres with π = 3.14.
a). basket ball b). tennis ball c). golf ball
3 m
Diametre = 24 cm Diametre = 4 cm Diametre = 68 mm
2. Find the volume and area of each of the following spheres in π.
a.
b.
c.
3. Find the radius of a sphere in which the volume is 288π cm3.
4. Find the radius of a sphere in which its surface area is 616 m2 and π =
7
22
.
Example
A sphere has radius of 3 cm, find its volume
and area of its side!
Solution:
V =
3
4
π r 3
=
3
4
π × 3 3
=
3
4
π × 3 × 3 × 3
= 36 π
A = 4 π r2
= 4π × 3 × 3 = 36π
So its volume is 36π cm3
and
the area of its side is 36π cm2
5 m
15 m
Mathematics for Junior High School Grade 9 / 49

7. 5. The earth has the shape of a sphere with a radius
of 6,400 km and 70% of its surface is water. Find
the area of the water surface (in km2).
6. A sphere-like balloon has a radius of 3 cm. The balloon is inflated to reach a
radius of 7 cm. Find the difference in volume between before and after it is
inflated.
7. A box is made to contain 12 tennis balls as
shown in the figure on the right. If the radius of
each ball is 4.6 cm, find the perimetre of the
smallest possible rectangle that will take the
balls.
/ Student’s Book – Space Figures with Curved Surface50