Tastey Tuesday!

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The London Eye is an observation wheel above the River Thames in London.  The diameter of the wheel is greater than 135 and less than 140 meters.  Describe the range of possible radii and circumferences of the wheel rounded to the nearest meter.

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VOLUME

So far, we have learned about length. This is a

measure of 1 dimension.

Measuring length can be as simple as measuring a straight

line segment.

5 inches

When you measure perimeter, you are also measuring length.

5 ft4 ft

3 ft

5 + 4 + 3 = 12 ft

When you measure circumference, you are also

measuring length.

4 cm 4 x 3.14 = 12.56cm

Area is a measure of 2 dimensions:

Length & Width

You can find the area of any FLAT shape.

5 cm

11 cm

5 x 11 = 55 square cm

You can even find the area of a circle.

5 cm 5 x 5 x 3.14 =

78.5 sq. cm

Volume is a measure of 3 dimensions:

LENGTH, WIDTH, & HEIGHT

Imagine starting with a piece of rectangular paper.

3 in

4 in

The area of this rectangle is 12 square inches

3 in

4 in

Now, suppose that we “stacked” another piece of paper on top of this

piece of paper.

3 in

4 in

3 in

4 in

3 in

4 in

3 in

4 in

3 in

4 in

3 in

4 in

Now we have 2 pieces of paper, each with an area of 12. So the

volume is 24.

3 in

4 in

Let’s add another piece of paper to the stack.

3 in

4 in

3 in

4 in

3 in

4 in

3 in

4 in

3 in

4 in

3 in

4 in

Now we have 3 pieces of paper, each with an area of 12. So the

volume is 36.

If we had 100 pieces of paper stacked on top of one another, what would the volume be?

4 in

3 in

100

4 x 3 x 100 = 1200

4 in

3 in

100

What are the units for volume?

Now that we are working with

all 3 dimensions, the units are cubes.

This is 1 cubic inch.1 x 1 x 1

1 in1 in

1 in

This is 2 cubic inches.2 x 1 x 1

2 in1 in

1 in

This is 4 cubic inches.2 x 1 x 2

2 in1 in

2 in

2 in2 in

2 in

8 cubic inches 2 x 2 x 2

Calculate the volume of this prism.

5 cm

8 cm6 cm

The volume is 240 cubic cm.6 x 5 x 8

5 cm

8 cm6 cm

Calculate the volume of this prism.

3 cm

12 cm5 cm

The volume is 180 cubic cm.5 x 3 x 12

3 cm

12 cm5 cm

Calculate the volume of this prism.

4 cm

11 cm7 cm

The volume is 308 cubic cm.7 x 4 x 11

4 cm

11 cm7 cm

Volume can also be described as AREA of the base x Height

V= Bh

Suppose that the area of this rectangle is 12.

4

3

Suppose that this rectangle served as the base of a

rectangular prism.

Suppose that the prism has a height of 2.

2

2

2

If the area (length x width) of the base is 12, and the height is 2…

2

then the volume should be 24 cubic units.

2

Therefore, if you know the area of the base and the height of the prism, then you can calculate the

volume.

SUMMARY

Volume = Length x Width x Height

Volume = Area of Base x Height

V = Bh

Practice Time!

1) Find the volume of the prism.

3 cm

3 cm

8 cm

The volume is 72 cm3.3 x 8 x 3

3 cm

3 cm

8 cm

2) Find the volume of the prism.

5 in

5 in

12 in

The volume is 300 in3.12 x 5 x 5

5 in

5 in

12 in

3) Find the volume of the prism.

2.5 ft

Area = 20 ft2

base

base

Volume = area x heightVolume = 20 x 2.5 = 50 ft3

2.5 ft

Area = 20 ft2

baseba

se

4) Find the volume of the prism.

14 m

Area = 12 m2

baseba

se

Volume = area x heightVolume = 12 x 14 = 168 m3

14 m

Area = 12 m2

base

base

5) Find the volume of the prism.

25 cm

Area = 15 cm2

basebase

Volume = area x heightVolume = 15 x 25 = 375 cm3

25 cm

Area = 15 cm2

basebase

6) Find the volume of the cylinder.

10 in

Area = 78.5 in2

base

base

Volume = area x heightVolume = 78.5 x 10 = 785 in3

10 in

Area = 78.5 in2

base

base

7) Find the volume of shape.

12 m

Area = 36.2 m2

basebase

Volume = area x heightVolume = 36.2 x 12 = 434.4 m3

12 m

Area = 36.2 m2

basebase

8) Find the volume of the triangular prism.

10ft15ft

8ft

Area of base = 8 x 10 ÷ 2 = 40 ft2

40 x 15 = 600 ft3

10ft15ft

8ft

9) Find the volume of the triangular prism.

8m12m

6m

8m12m

6m

Area of base = 6 x 8 ÷ 2 = 24 ft2

24 x 12 = 288 m3

10) Find the volume of the triangular prism.

7 cm11 cm

6cm

7 cm11 cm

6cm

Area of base = 6 x 7 ÷ 2 = 21 ft2

21 x 11 = 231 m3

11) Find the volume of the cylinder.

6 in

3 in

Area of base = 3 x 3 x 3.14 = 28.26 in2

28.26 x 6 = 169.56 in3

6 in

3 in

12) Find the volume of the cylinder.

8 km

5 km

8 km

5 km

Area of base = 5 x 5 x 3.14 = 78.5 km2

78.5 x 8 = 628 km3

13) Find the volume of the cylinder.

11 m

8 m

11 m

8 m

Area of base = 8 x 8 x 3.14 = 200.96 m2

200.96 x 11 = 2210.56 m3

Homework:Complete Worksheet

Practice A/ B/ C/ Problem Solving