Difference between revisions of "Geogebra/C3/Mensuration/English"

Welcome to this tutorial on Mensuration in Geogebra.

Learning Objectives

In this tutorial, we will learn to find

• Area and perimeter of rhombus

• Surface area of sphere and cone

• Volume of sphere and cone

Pre-requisites

For Revelant tutorials on Geogebra,

Please visit our website

http://spoken-tutorial.org

System Requirement

To record this tutorial I am using

Ubuntu Linux OS Version 11.10

Geogebra Version 3.2.47.0

Tools used in the tutorial

• Segment between two points

• Circle with center and radius

• Ellipse

• Polygon

• New point and

• Insert text

Dash home>> Media Apps>>Eduaction>>Geogebra

Click on Dash home and Media Apps. Under Type, choose Education and Geogebra

Let's use the file quadrilateral.ggb of the previous tutorial

click on 'Open'

“Area of the rhombus =”+(1/2 g f)

Area of the rhombus = close the double quotes

'+' for concatenation open the brackets type

'1/2' space 'f' space 'g'

close the bracket

'f' and 'g' are diagonals of the rhombus

Point to the Area of rhombus

Area of rhombus is displayed here on the drawing pad.

Click “Insert text” tool

Click on the “Insert text” tool

“Perimeter of the rhombus =”+(4 a)

Perimeter of the rhombus =

close double quotes '+' open the brackets

'4' space 'a' close the brackets

'a' is side of the rhombus

Point to perimeter of rhombus

Perimeter of rhombus is displayed here on the drawing pad.

Click on “File” and "Save As".

I will type the filename as "rhombus-area-perimeter"

Click on “Save”.

Assignment 1

To find area and perimeter of trapezium,

use output of file “cons-trapezium.ggb”

Rename object 'g' as 'b'

Formula for area = (half sum of parallel sides) * (vertical height) = (a+b)/2* h

Formula for perimeter =(sum of the sides) =(a+b+c+d)

Click on “File” , “New”

enter value '2' for radius.

A circle with center 'A' and radius '2cm' is drawn.

Click “Segment between two points” tool>> join 'A' and 'B'

Join points 'A' and 'B' as radius of the circle

to touch the circumference of the circle.

and a third point 'E' inside the circle

Here a sphere is drawn

Click on “Insert text” tool

Click on “Insert text” tool

Scroll down the list to find π (pi)

Please use drop down list in the text box for special characters

Scroll down the list to find π (pi)

“ Surface area of the sphere =” +( 4 π a^2)

Surface area of the sphere =

close double quote 'plus' open the bracket '4' space

select 'π' from the list space

'a' select 'square' from the list

close the bracket

surface area of the sphere is displayed here

let me click on it and drag it place it below

Insert another text box

Text box opens

Volume of the sphere =

close double quote 'plus' open the bracket '4/3' space

select 'π' from the list space 'a'

select 'cube' from the list close the bracket

Volume of the sphere is displayed here

let me click on it and drag it to place it below

Click Polygon tool>>Click on 'C' , 'D', 'F' and 'C'

Click on points 'C' , 'D' and an external point 'F'

and 'C'once again

to join points 'A' and 'F'

We get height of the cone.

Right click on the object>>select “Rename”

Replace 'b with 'h'

Right click on object 'b'

Click on “Rename”

Replace 'b' with 'h' click OK

Rename the object 'c_1' as 's' which denotes slant height of cone.

Right click on 'c_1'

click on “Rename”

Replace 'c_1' with 's'

Click OK

We can use either the Insert text tool from the tool bar or we can the input bar.

I will use the “Input bar”

Scroll down the list.

Click on “π”

Please find the special characters in the drop down list of “Input bar”

Scroll down to find “π”

Type in the input bar

Select 'π' from the list space 'a' space 's'

plus select 'π' from the list space 'a'

Select 'square' from list close the bracket

press enter

Please note when we use the Input bar

answer appears in the Algebra view

Volume =(1/3 π a² b)

'1/3' space select 'π' from the list space 'a'

Select 'square' from list space 'h' close the bracket

Press enter

I will type the filename as "Sphere-cone"

Click on “Save”.

with this we come to the end of this tutorial

Summary

In this tutorial we have learnt to find

• Find Area and perimeter of rhombus

• Surface Area of sphere and cone

• Volume of sphere and cone

We have also learnt to draw sphere and cone

Assignment

As an assignment I would like you to find Surface area and volume of cylinder

Draw 2 same sized ellipses one below the other

Connect edges of ellipses

Use “center” tool, find center of one ellipse

Join center and edge.

Rename object 'b' as 'h' and 'e' as 'r'

Surface area = 2 π r(r + h)

Volume = π r^2h

Acknowledgement

http://spoken-tutorial.org/What is a Spoken Tutorial

It summarises the Spoken Tutorial project

If you do not have good bandwidth, you can download and watch it

Conducts workshops using spoken tutorials

Gives certificates to those who pass an online test

For more details, please write to

contact@spoken-tutorial.org

It is supported by the National Mission on Education through ICT, MHRD, Government of India

More information on this Mission is available at http://spoken-tutorial.org/NMEICT-Intro ]

This is Madhuri Ganapathi from IIT Bombay signing off.

Thanks for joining