UDAYA COLLEGE OF UDAYA COLLEGE OF

EDUCATIONEDUCATION

UDAYA NAGERUDAYA NAGER

AMMANDIVILAIAMMANDIVILAI

NAME NAME : A AMMU BITIYA: A AMMU BITIYA

SUBJECTSUBJECT : MATHEMATICS: MATHEMATICS

ROLL NOROLL NO ::

spheresphere

spheresphere

Definition:Definition:

A semicircle when revolved A semicircle when revolved

about its diameter which is kept about its diameter which is kept

fixed, a solid will be generated. fixed, a solid will be generated.

This solid is called a sphere.This solid is called a sphere.

Examples of sphere Examples of sphere

Some of the objects from our Some of the objects from our

daily life which brings to our mind the daily life which brings to our mind the

concept of sphere is ball, globe, concept of sphere is ball, globe,

lemon and shot put etc.lemon and shot put etc.

Diameter of the sphereDiameter of the sphere

A line segment passing through the center A line segment passing through the center

of the sphere and having its end points on the of the sphere and having its end points on the

sphere is called the diameter of the sphere.sphere is called the diameter of the sphere.

BB

OO

AA

AOB is the diameter AOB is the diameter

Center and radius of the sphereCenter and radius of the sphere

The sphere is generated by one complete The sphere is generated by one complete

revolution of the semi-circle AOB about the revolution of the semi-circle AOB about the

diameter AOB. The center and radius of the diameter AOB. The center and radius of the

semi circle are the center and radius of the semi circle are the center and radius of the

sphere.sphere.

HemisphereHemisphere

Definition:Definition:

A section of a sphere produced by A section of a sphere produced by

a plane is a circle. The circle, which passes a plane is a circle. The circle, which passes

through the center of the sphere is the largest through the center of the sphere is the largest

circle. It divides the sphere into two equal circle. It divides the sphere into two equal

parts. Each part is called hemisphere. parts. Each part is called hemisphere.

Illustration of surface area of the Illustration of surface area of the

hemispherehemisphere

The length of the string used to cover the The length of the string used to cover the

entire hemisphere is twice the length of the entire hemisphere is twice the length of the

string used to cover the circular region.string used to cover the circular region.

RemarkRemark

In case of sphere, the In case of sphere, the

curved surface area and the curved surface area and the

total surface area are the total surface area are the

same.same.

Volume of the sphereVolume of the sphere

•Volume of the sphereVolume of the sphere

= 4/3 = 4/3 rr33 Cu. Units. Cu. Units.

Volume of hemisphere Volume of hemisphere

Volume of hemisphereVolume of hemisphere

== ½ ½ volume of sphere volume of sphere

== ½ ½ 4/3 4/3rr33

= = 2/32/3rr3 3 Cu.units Cu.units

Examples:-Examples:-

1. Radius of the sphere is 4 m. Find its 1. Radius of the sphere is 4 m. Find its surface areasurface area

Given : Surface area of the sphere Given : Surface area of the sphere

= 4= 4 rr22

= 4 = 4 x x 16 x 16

= 64 = 64 mm22

POST TESTPOST TEST

1.1. Define sphere?Define sphere?

2.2. What is the surface area of the What is the surface area of the

hemisphere?hemisphere?

3.3. What is the surface area of the sphere? What is the surface area of the sphere?

RESPONSESRESPONSES

1.1. A semicircle when revolved about its A semicircle when revolved about its

diameter which is kept fixed, a solid will diameter which is kept fixed, a solid will

be generated. This solid is called a be generated. This solid is called a

sphere.sphere.

2.2. Surface area of the hemisphere = 2Surface area of the hemisphere = 2rr22 Sq. Sq.

units.units.

3.3. Surface area of the sphere = 4Surface area of the sphere = 4rr2 2 Sq. units.Sq. units.