Finding Volume Finding Volume of Solid Figuresof Solid Figures

Ms. Julien

East Cobb Middle School

First…First…

What are we talking about What are we talking about when we talk about VOLUME of solid figures?when we talk about VOLUME of solid figures?

a.a. The sound that comes from your TV or IPodThe sound that comes from your TV or IPod

b.b. The concept of having full, bouncy hairThe concept of having full, bouncy hair

c.c. A collection of written documents (ie., A collection of written documents (ie., newsletters, encyclopedias, etc.)newsletters, encyclopedias, etc.)

d. The amount of space inside a solid figured. The amount of space inside a solid figure

That’s right! Give yourself a pat on That’s right! Give yourself a pat on the back!the back!

Volume of a solid figure Volume of a solid figure refers to the amount of refers to the amount of

space inside a solid figure.space inside a solid figure.

What are some examples??What are some examples??

Water needed to fill a poolWater needed to fill a pool

The amount of jelly inside a jarThe amount of jelly inside a jar

The amount of space inside a car’s trunkThe amount of space inside a car’s trunk

Air inside a maskAir inside a mask

Clothes inside a suitcaseClothes inside a suitcase

Ice cream inside a coneIce cream inside a cone

Volume is measured in cubic unitsVolume is measured in cubic units. This . This basically means that you are finding how many basically means that you are finding how many cubes you could fit inside the object.cubes you could fit inside the object.

So, what is the Volume of this So, what is the Volume of this Rectangular Prism?Rectangular Prism?

In other words, how many cubes In other words, how many cubes could fit inside?could fit inside?

How did you get that answer?How did you get that answer?

You multiplied 3 x 6, and then multiplied that You multiplied 3 x 6, and then multiplied that product by 4. product by 4.

So, the volume of this rectangular prism is So, the volume of this rectangular prism is 72 cubic units.72 cubic units.

Let’s analyze this to determine the Let’s analyze this to determine the formula…formula…

What does What does 3 3 • 6• 6 give us?give us?

Area of the rectangular base,Area of the rectangular base,good!good!

Then we multiplied the area of the base by the height Then we multiplied the area of the base by the height This means we are basically “filling up” the figure, or This means we are basically “filling up” the figure, or finding the volume.finding the volume.

V = V = l l • • ww • • h h oror V = V = BhBhV = Area of the base x heightV = Area of the base x height

VolumeVolume

Find the volume of this prism…Find the volume of this prism…

Formula:

V = B x hV = l x w x h

5 cm4 cm

7 cm

VolumeVolume

Find the volume of this prism…Find the volume of this prism…

Formula:

V = B x hV = l x w x h

V = 5cm x 4cm x 7cm

5 cm4 cm

7 cm

VolumeVolume

Find the volume of this prism…Find the volume of this prism…

Formula:

V = B x hV = l x w x h

V = 5cm x 4cm x 7cm

V = 140cm35 cm4 cm

7 cm

VolumeVolume

Volume of a Triangular PrismVolume of a Triangular Prism

VolumeVolume

The same principles apply to the The same principles apply to the triangular prism.triangular prism.

To find the volume of the triangular prism, we must first find the area of the triangular base (shaded in yellow).

b

h

VolumeVolume

Now to find the volume…Now to find the volume…

We must then multiply the area of the base (B) by the height (h) of the prism.

This will give us the Volume of the Prism.

B h

VolumeVolume

Your turn…Your turn… Find the Volume

How can I find the volume of a How can I find the volume of a square pyramid?square pyramid?

Let’s Let’s Experiment!Experiment!

Volunteers:Volunteers:

1.1. Compare the characteristics of the prism Compare the characteristics of the prism and the pyramid. (ie, length, width, height)and the pyramid. (ie, length, width, height)

2.2. Fill the pyramid completely with water. Fill the pyramid completely with water.

3.3. Dump the water from the pyramid into the Dump the water from the pyramid into the prism. prism.

4.4. Continue until the prism is full.Continue until the prism is full.

5.5. What do you observe? What do you think is What do you observe? What do you think is the formula for volume of a pyramid?the formula for volume of a pyramid?

Volume of a Pyramid

(Area of Base x Height)

3

(Area of Base x Height)

1 3

click to reveal

A pyramid is 1/3 the volume of a prism with the same base area (B) and height (h).

Pyramids are named by the shape of their base..

The volume is a pyramid is 1/3 the volume of a prism with the same base area(B) and height (h).

V = Bh13

=5 m

side length = 4 m

V = Bh13

How can I find the How can I find the volume of a square volume of a square

pyramid?pyramid?

If you said If you said

V = 1V = 1/3 /3 •• BhBh……

GOOD JOB!GOOD JOB!

So… what is volume?So… what is volume?

The amount of space, The amount of space, measured in cubic measured in cubic units, of a 3D solid units, of a 3D solid

figure.figure.

Volume Formula Recap:Volume Formula Recap:

Prisms:Prisms:V = BhV = Bh

Pyramids:Pyramids:V = 1/3 BhV = 1/3 Bh

On all of these, B stands for “Area of the On all of these, B stands for “Area of the Base”. So, you must determine what Base”. So, you must determine what shape the base is and use the correct shape the base is and use the correct formula to get the area of the base. formula to get the area of the base. Then, complete the formula.Then, complete the formula.

You do not have to memorize these You do not have to memorize these formulas… however, you must formulas… however, you must understand how to use them!understand how to use them!

In other words, if given a formula and the In other words, if given a formula and the numbers you need for the variables numbers you need for the variables (length, width, height, radius, etc.), could (length, width, height, radius, etc.), could you find the volume of a rectangular prism, you find the volume of a rectangular prism, square pyramid, cylinder, or a cone?square pyramid, cylinder, or a cone?

8 cm

7 cm

15.3 cm

Find the volume

Find the Volume of a triangular pyramid with base edges of 8 in, base height of 4 in and a pyramid height of 10 in.

8 in

10 in

4 in

The Pyramid of Kukulcán in The Pyramid of Kukulcán in Mexico is a square pyramid. Mexico is a square pyramid.

Its height is 24 m and its Its height is 24 m and its base has 55 m sides. Find base has 55 m sides. Find

the volume of the pyramid.the volume of the pyramid.