The Smartest Friend I Had

A Micr o-lesson on Volumes of Solid Figures Prepared by: amelia a. colorado

Objectives: At the end of this micro lesson, you (students) will be able to:  Solve for the volumes of any solid figures.  Determine what formula you are going to use in every problems you have to solve.

T he Smar test Friend I ever had

Once upon a time in a faraway land called Minitopia there lived a bear named Michael. Michael is a happy bear!

Woohooo! I love to do this!

He loves to eat honey! And he has a friend named Johnny.

Hello Michael!

Hi Johnny!

One day Johnny found Michael wearing a sad look in his face. You look sad. What's your problem?

My Honey is gone! And I'm afraid I can’t get another jar of honey!

Johnny told Michael not to worry because he knew a secret place where there are lot’s of honey! With no waste of time they started to go to the secret place.

After sometime, they reached the secret place. However,

What are you doing in my place?

Are you the owner of this place? I heard that you have lot’s of honey. Can I ask for some?

What makes you think I’ll give you my honey! You must have also heard that you need to give something in exchange for my honey

So what do you want then?

From a good bear like you, I only want you to give me 2 pieces of bread in exchange for my delicious and yummy honey.

Do we have a deal?

Michael gave 2 pieces of bread to the owner of the secret place and…

Yahoo! Now I can have all the honey I want!

Hep,hep,hep. I’ll only allow you to use one container for the honey you want to get.

Choose wisely among these six containers

If you want to get lot’s of honey, you need to choose the container that has the biggest volume! (click this)

What container am I going to choose? Johnny do you have an idea?

Thanks Johnny! You’re really the smartest friend I ever had! Now I know how to find the volumes of different solid figures

Now I know what container I have to choose!

 The volume of any solid, liquid, plasma, vacuum or theoretical object is how much threedimensional space it occupies, often quantified numerically.  Volume is commonly presented in units such as mL or cm3 (milliliters or cubic centimeters).  Volumes of some simple shapes can be computed by just multiplying it’s base area with its height. Click me

The volume of a cylinder is found by multiplying the area of one end of the cylinder by its height. Or as a formula: r = 2m h = 2m V= Пr^2h where: π is Pi, approximately 3.142 r is the radius of the circular end of the cylinder h height of the cylinder Click me

The volume of a cube is found by multiplying the length of any edge by itself twice. So if the length of an edge is 4, the volume is 4 x 4 x 4 = 64 Or as a formula: V = s^3 where: s is the length of any edge of the cube (The base and sides of a cube is a square)

s = 3m Click me

Solution for the volume of the cylindrical container: r = 2m

The base of a h = 2m cylinder is a circle.

Since r = 1m and h =1m then, using the formula for finding the volume of the cylinder we have: V= Пr^2h (Пr^2 is just the area of it’s base) = ( 3.142) (2m)^2(2m) = 25.12 m^3 click me first

Click after

Solution for finding the volume of the cubical container:

s = 3m

Since the sides (s) of this container is 3m then, V = s^3 = (3m)^3 = 27 m^3 click me first

Click after

The volume of a sphere is found by using the formula: V = 4/3 (Пr^3) ( Where r is the radius of the sphere r = 1.5 m

Using the formula of a sphere, the volume of this spherical container is: V = 4/3 (3.142)(1.5m)^3 = 14.14 m^3 Click me

The volume V of any cone with radius r and height h is equal to one-third the product of the height and the area of the base. Formula: V = (1/3)(PI)r^2h where r = radius of it’s base h = height of the cone

Click me

To compute for the volume of the conical container, we have to use the formula for finding the volume of a cone which is: V = (1/3)(PI)r^2h = (1/3)(3.142)(2.5m^2)(4m) = 26.18 m^3 Examples of cones:

Click me

In geometry, a square pyramid is a pyramid having a square base. The formula to find the volume of a square pyramid is: V = Bh/3 where B = area of the base (square) Click me

For us to solve for the volume of the of the container with a square pyramid shape, we have to use the formula for finding the volume of a square pyramid: V = Bh/3 = s^2(h)/3 = (3m^2)(6m)/3 = 18 m^3 s = 2m ; h = 3m

Click me

Hey mister monkey! You can’t fool me anymore ‘coz I already know how to solve for the volumes of your containers and I know which one has the largest volume!

I’m going to choose the cubical container!

You really deserve this amount of honey! You’re not only a good bear ! you’re also a smart one!

HONEY

hey smart one! click me.

References: http://www.ohiorc.org/orc_documents/orc/RichPro blems/Discovery-Volumes_Experimentally.pdf http://www.gifs.net/image/Animals/Bears_and_Pan das/Bear_face/4720 http://www.mathguide.com/lessons/Volume.html http://www.math.com/school/subject3/lessons/S3U 4L4DP.html

Thank you! Bye ! ‘Til next time