CHAPTER: VOLUME AND SURFACE AREA STD: VIII

CHAPTER: VOLUME AND SURFACE AREASTD: VIII

SUBJECT: MATHSPRESENTED BY : MONA A. PATILROLL NO.: 68YEAR: 2011-2012

CONTENTS

INTRODUCTION

In previous class we have studied about volume and surface area of a cylinder.

What do we called this shape?

Triangle

Cone

Cylinder

Today we are going to study about the volume of a Cone.

A cone has one circular flat surface and one curved surface.

In the diagram alongside,

seg OA (h) is the height of the cone.seg AP (r) is the radius of the cone.seg OP (l) is the slant height of the cone.

In diagram alongside A = 90

AOP

In the diagram alongside B = 90

BAC

The angle between the height of the cone and a radius of the base is a right angle.

The measure of the space occupied by any cone is called volume of the Cone.

Volume of a Cone =1/3 x area of base x height.

Base of a Cone is a circle.What is the area of a circle?

r2

2r

d

Area of base = r2

volume of a cone = 1/3 xr2x h = 1/3 r2h

The height of a cone is 14cm and the radius of its base is 3cm. What is its volume?Solution : Here, r= 3cm, h= 14cmVolume of cone = 1/3r2h = 1/3x 22/7 x 3x3 x14 = 22x 3 x9 = 132 cu.cm

2. Find the volume of a cone of height 7cm and a base radius of 9cm.

Solution: Here, r = 9cm , h = 7cmVolume of Cone = 1/3r2h = 1/3 x 22/7 x 9 x 9 x 7 = 22 x 3 x9 = 594 cu. cm

3.The radius of the base of a cone is 5cm and its slant height is 13cm. Find the volume of the cone.(=3.14)

Solution: here r=5cm, l=13cmTo find out the volume of the cone we require height(h) of the cone.

The height and the radius of a cone form a right angle.

So we will use Pythagoras theorem to find out he height of the cone.

Using Pythagoras theorem l2 = r2 + h2 132 = 52 + h2 h2 = 132 52 h2 = 169 25 h2 = 144 h = 12

Volume of a cone = 1/3r2h= 1/3 x 3.14 x 5x5x12= 942/3= 314 cu.cm.

VALUE :Volume is the capacity of an object to hold , like that we also have capacity to hold our anger and joy.

The height and the radius of a cone form a ______angle.obtuse

acute

right

Volume of a cone =..

r2

r2h

1/3r2h

1.find the volume of a cone of height 18 cm and a base radius of 7 cm.

Here , r= ? and h= ?

18 and 7

7 and 18

r =7 and h = 18

Volume of a cone = 1/3r2h = 1/3 x 22/7 x 7 x 7 x18 = 1 x 22 x 7 x 6 = 22 x 42

hence , volume of a cone =.

448 cu. cm

924 cu. cm

846 cu.cm

CongratulationYour answer is right.

WRONG

CongratulationYour answer is right.

WRONG

CongratulationYour answer is right.

WRONG

CongratulationYour answer is right.

WRONG

CongratulationYour answer is right.

WRONG

CongratulationYour answer is right.

WRONG