KCSE ONLINE

One stop Education solutions

My ADS

Last Photo

Social Media

   

Revision


 Other 

Candidate benefit from our revision notes which are comprehensive and show how to tackle examination questions effectively


Results


 Moreover 

As a supplementary to coursework content our e-library for digitized multimedia CDs while enhance and ensure that you never missed that important concept during the normal class lessons. It is a Do it Yourself Project


KNEC


 Adobe  

For Best results INSTALL Adobe Flash Player Version 16 to play the interactive content in your computer. Test the link below to find out if you have Adobe Flash in your computer


Volume of Solids

 

 

 

 

LESSON OBJECTIVE

By the end of the lesson the you should be able to find the

volume of a frustrum.

Introduction

Volume of a cone

To find the volume of the above cone you proceed as follows

Example 1
Find the volume of a cone whose slant height is 6cm and radius is 4cm.

We use pythagoras theorem to find height of the cone i.e.

= 36-16= 20

h = 4.4721cm
h = 4.472cm
Therefore the area of cone = base Area x height

 =74.94cm3            

volume of a pyramid
   

The volume of the pyramid is worked our as follows
V =
Therefore, if the height is 12cm, the base length 5cm and width 4cm
Volume =
=128cm3
 

Introduction

Volume of a cone

To find the volume of the above cone you proceed as follows

Example 1
Find the volume of a cone whose slant height is 6cm and radius is 4cm.

We use pythagoras theorem to find height of the cone i.e.

= 36-16= 20

h = 4.4721cm
h = 4.472cm
Therefore the area of cone = base Area x height

 =74.94cm3            

volume of a pyramid
   

The volume of the pyramid is worked our as follows
V =
Therefore, if the height is 12cm, the base length 5cm and width 4cm
Volume =
=128cm3
 

Volume of a Cone

To find the volume of the above cone you proceed as follows Example 1 Find the volume of a cone whose slant height is 6cm and radius is 4cm. We use Pythagoras theorem to find height of the cone i.e. = 36-16= 20 h = 4.4721cm h = 4.472cm Therefore the area of cone = base Area x height =74.94cm3

Volume of a frustum
A frustum is obtained ,when a cone or pyramid is cut along a plane parallel to the base shown below:
Example
 

Find the volume of the given frustum whose top radius is 6cm,and bottom
Radius is 2cm and the height is 10cm

Solution
To obtain the volume of the above frustum ABCD, we have to get the vertical ,height h of the smaller cone DCV.
We know that the smaller cone DCV is similar to the bigger cone ABV hence the ratio of their corresponding sides are equal. Type equation here.


6h=2(10+h)
6h =20 + 2h
4h =20
H= = 5cm
Volume of cone = h
Volume of bigger cone ABV
= x 3.142 x 6 x 6 x 15
=565.56cm3
Volume of smaller cone DCV
x 3.142 x2 x 2 x5
=20.95 cm3
Therefore the volume of frustum =volume of bigger cone ' volume of smaller cone.
=(565.56 -20.95) cm3
=544.61cm3
 

Exercise
1. find the volume of the lampshade the shape of a frustrum whose bottom radius 12cm,top radius 6cm and slant height is 10cm


 

Diag(a)
Solution
Diag(b)
 


Complete the missing part of the cone.
Then find L the slant height of the small cone using the ratio of the corresponding of sides of the similar cones i.e.
= = =
12L= 6(10 +c)
12L=60 + 6L
6L = 60
L =10
STEP2
Using the information derived find H-the vertical; height of the bigger cone.
 

H=
=
=
=16
STEP 3.
Find the vertical height of the small cone
Using the corresponding radios
= = =
12h =96
h= 8
step4:
volume of the bigger cone

= cm3
Volume of smaller cone
=
= cm3
Volume of the frustum = volume of bigger cone ' volume of smaller cone.
= 2413.056 - 301.632cm3
= 2111.424 cm3
2. Find the volume of the given frustum which has a square base of 6cm and a top has
Sides 2cm.the height of the frustum is 12cm.
 


 

Solution
To find the volume of the frustum using dotted lines and the vertec v, then find the volume of big and small pyramids.
(use different colour for dotted height)

 

Diag(d)


6h =2(12 +h)
6h =24 + 2h
4h =24
h =6
Therefore, height of the bigger pyramid =12 +6=18
volume of smaller pyramid=
=
= 216 cm3
Volume of smaller pyramid =
=
= 24 cm3
Volume of the frustum = volume of larger pyramid ' volume of small pyramid
=(216 ' 24) cm3
=192cm3

 

 

 



 Volume of Solids 

 e-Content 

Buy e-Content Digital CD covers all the topics for a particular class per year. One CDs costs 1200/-


click to play video

Purchase Online and have the CD sent to your nearest Parcel Service. Pay the amount to Patrick 0721806317 by M-PESA then provide your address for delivery of the Parcel.. Ask for clarification if in doubt,




























 Volume of Solids  

Candidate benefit from our quick revision booklets which are comprehensive and how to tackle examination question methods
We have an enourmous data quiz bank of past papers ranging from 1995 - 2017 


KCSE ONLINE WEBSITE provide KCSE, KCPE and MOCK Past Papers which play a great role in students� performance in the KCSE examination. KCSE mock past papers serves as a good motivation as well as revision material for the major exam the Kenya certificate of secondary education (KCSE). Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE . Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE. It is also cost effective

MOCK Past Papers


As a student, you will have access to the most important resources that can help you understand what is required for you to sit and pass your KCSE examination and proceed to secondary school or gain entry to University admission respectively. 

www.kcse-online.info


KCSE ONLINE

 Similar  

  More  

 Similar  

KCSE ONLINE WEBSITE provide KCSE, KCPE and MOCK Past Papers which play a great role in students� performance in the KCSE examination.

Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE. It is also cost effective 

Ask for clarification if in doubt, vitae dignissim est posuere id.

 Volume of Solids 




sit amet congue Mock Past Papers, give you an actual exam situation in readiness for your forthcoming national examination from the Kenya National Examination Council KNEC

Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE. It is also cost effective sapien. 

Choosing the KCSE mock examination revision material saves you a lot of time spent during revision for KCSE. It is also cost effective sapien. 



 Volume of Solids

As a supplementary to coursework content our e-library for digitized multimedia CDs while enhance and ensure that you never missed that important concept during the normal class lessons. It is a Do it Yourself Project..

Candidates who would want their papers remarked should request for the same within a month after release of the results. Those who will miss out on their results are advised to check with their respective school heads and not with the examination council

For Best results INSTALL Adobe Flash Player Version 16 to play the interactive content in your computer. Test the link below to find out if you have Adobe Flash in your computer. 


Search

My ADS

New Register


 Similar  

Buy e-Content Digital CD covering all the topics for a particular class per year. One CDs costs 1200/- ( Per Subject per Class )


New Membership


  Also

 

We have an enourmous data quiz bank of past papers ranging from 1995 - 2017


Register


 Gold 

 

Register as gold member and get access to KCSE and KCPE resources for one year. subscription is 1000/- renewable yearly.

Click Here to Register

neravaren