Transcript
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.
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