1 of 20

Welcome

JAWAHAR NAVODAYA VIDYALAYA

LEPAKSHI

ANANTAPUR DISTRICT

2 of 20

COORDINATE GEOMETRY

​

CLASS :X

CBSE

TOPIC: VOLUME

BY G.SUMATHI

TGT MATHEMATICS

JNV ANANTAPUR

SURFACE AREA AND VOLUME

3 of 20

4 of 20

VOLUME

Volume is the amount of space occupied by any 3-dimensional object

5 of 20

VOLUME OF

  • Cuboid
  • Cube
  • Cylinder
  • Cone
  • Sphere
  • Hemi spher
  • Frustum of a cone

6 of 20

Side 2

Bottom

Back

Top

​

Side 1

​

Front

Side 2

Bottom

Back

Top

​

Side 1

​

Front

Length (L)

Breadth (B)

Height (H)

Cuboid

Dimensions of cuboid

7 of 20

Side 2

Bottom

Back

Top

​

Side 1

​

Front

Side 2

Bottom

Back

Top

​

Side 1

​

Front

Length (L)

Breadth (B)

Height (H)

Volume of Cuboid

Volume= Base area x Height

=(LxB)xH

V = LxBxH Cubic units

8 of 20

Cube

9 of 20

VOLUME OF CUBE

  • Volume=Base areax height

= a2 x a

= a3 cubic units

a

a

a

10 of 20

What Is Volume of cylinder ?

The volume of a solid is the amount of space inside the solid.

Consider the cylinder below:

If we were to fill the cylinder with water the volume would be the amount of water the cylinder could hold:

r

h

Dimensions

11 of 20

The Volume Of A Cylinder.

rcm

h

Volume = Base areax Height

V = ∏ r 2 x h cubic units

r = Base Radius h = Height.

12 of 20

Volume Of A Cone.

The diameter (D) of the top of the cone and the cylinder are equal.

D

D

The height (H) of the cone and the cylinder are equal.

H

H

If you filled the cone with water and emptied it into the cylinder, how many times would you have to fill the cone to completely fill the cylinder to the top ?

3 times.

This shows that the cylinder has three times the volume of a cone with the same height and radius.

13 of 20

The experiment on the previous slide allows us to work out the formula for the volume of a cone:

The formula for the volume of a cylinder is :

V = ∏ r 2 h

We have seen that the volume of a cylinder is three times than that of a cone with the same diameter and height .

The formula for the volume of a cone is:

h

r

r = radius h = height

14 of 20

Calculate the volume of the cones below:

13m

18m

(2)

9m

6m

(1)

15 of 20

volume of sphere

​

​

​

  • Volume =

r

16 of 20

volume of Hemi sphere

​

​

​

  • Volume =

r

∏r3

r

17 of 20

FRUSTUM OF A CONE

18 of 20

rr

l=slant height

Height=h

r

R

Frustum of a cone

Volume of Frustum of a cone

If Radius of smaller

circular base=r

If Radius of bigger

circular base=R

Perpendicular distance

Between two circular faces=h

Slant height =l

Volume of Frustum=

∏ (r2+R2+rR)h cubic units

Relation between l,h,r,R is l2= h2+ (R-r)2

19 of 20

Summary Of Volume Formula.

l

b

h

V = l b h

r

h

V = ∏ r 2 h

h

r

20 of 20

Than you

one and all