MATHEMATICS

MATHEMATICS

DIGITAL TEXT BOOK

CLASS X

Submitted by,

ANCY BABY

B.Ed Mathematics

Reg no: 18014350003

CHAPTER – 1

CIRCLES

Circle is a shape which is very important magnificent and having many peculiarities. Of the closed figures having the same circumference, the circle deserves more importance since it has a greater area. The photos of celestial bodies and the shape of the wheel and most of the flowers are circular.

RIGHT ANGLE AND CIRCLES

If the ends of a diameter of a circle are joined to any other points on the circle, then what we get is a right angle.

ANGLE AND ARCS

Y

A B

X

AB divides the circle into two arcs AYB and AXB.

The angle made by an arc at any point on the alternate arc is equal to half the angle made at the center.

A

Q

B

AOB=280

AQP=140

SEGMENTS OF A CIRCLE

B

C

A

P

ABC is a segment. APC is another segment.

Angles in same segment are equal.

If all the vertices of a quadrilateral are on a circle, then its opposite angles are supplementary.

CUTTING CHORDS

C

A B

D

AB is the diameter and CD is a chord perpendicular to it :

Then ,

AO OB = CO2

EXERCISE

In triangle ABC, we have A = 60

and B = 70 is the vertex C is inside or outside with diameter AB.

Prove that is a pair of opposite angles of a quadrilateral is right, and then a circle can be drawn through all four of its vertices.

Prove that non isosceles trapeziums are not cyclic.

CHAPTER 2

SOLIDS

PYRAMIDS

General name of such solids are called pyramids.

The sides of the polygon forming the base of a pyramid are called the base edge and the other sides of the triangles are called lateral edges . the top of a pyramid is called its apex .

Apex

Lateral edge

Base edge

SURFACE AREA OF A PYRAMID

Surface area of a pyramid is the sum of the surface area of the square base and surface area of the 4 triangle faces.

Surface area of a square pyramid

=2bs+b2

Find the surface area of a squarepyramid of base length 3cm and slant height 5cm?

Surface area of a squre pyramid

= 2bs+b2

= 2×3×5+32

=39cm2

VOLUME OF A PYRAMID

The volume of a square pyramid is a third of the product of its base area and height.

The volume of a pyramid =?? b2h

Find the volume of a square pyramid of base edge 10cm and height 8cm?

The volume of a square pyramid

=?? b2h

=?? ×102× 8

=266?? cm3

CONES

Such a solid is called cones.

VOLUME OF A CONE

The volume of a cone is the product of its base area and height.

Find the volume of a cone with base radius 4cm and height 6cm?

Base area=4 × 4=16cm

Height =6cm

Volume=?? ? ×42×6

=32? cu.cm

SPHERES

The surface area of a sphere is the product of its radius by 4

Surface area of a sphere =4πr2

What is the surface area of the largest sphere that can be curved out from a cube of side 8cm?

Surface area of sphere = 4πr2

=4? ×42

=64πcm2

VOLUME OF A SPHERE

Volume of a sphere = ??πr3

EXERCISE:

1) Find the surface area of a squre pyramid of base length 6cm and slant height 10cm?

2) Find the volume of a square pyramid of base edge 12cm and height 10cm?

3) Find the volume of a cone with base radius 8cm and height 10cm?