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 ft 4 ft 3 ft = 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 = 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 in

This is 2 cubic inches. 2 x 1 x 1 2 in 1 in

This is 4 cubic inches. 2 x 1 x 2 2 in 1 in 2 in

8 cubic inches 2 x 2 x 2

Calculate the volume of this prism. 5 cm 8 cm 6 cm

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

Calculate the volume of this prism. 3 cm 12 cm 5 cm

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

Calculate the volume of this prism. 4 cm 11 cm 7 cm

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

Volume can also be described as AREA x Height

Suppose that the area of this rectangle is

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 or Volume = Area of Base x Height

Practice Time!

1) Find the volume of the prism. 3 cm 8 cm

The volume is 72 cm 3. 3 x 8 x 3 3 cm 8 cm

2) Find the volume of the prism. 5 in 12 in

The volume is 300 in x 5 x 5 5 in 12 in

3) Find the volume of the prism. 2.5 ft Area = 20 ft 2 base

Volume = area x height Volume = 20 x 2.5 = 50 ft ft Area = 20 ft 2 base

4) Find the volume of the prism. 14 m Area = 12 m 2 base

Volume = area x height Volume = 12 x 14 = 168 m 3 14 m Area = 12 m 2 base

5) Find the volume of the prism. 25 cm Area = 15 cm 2 base

Volume = area x height Volume = 15 x 25 = 375 cm 3 25 cm Area = 15 cm 2 base

6) Find the volume of the cylinder. 10 in Area = 78.5 in 2 base

Volume = area x height Volume = 78.5 x 10 = 785 in 3 10 in Area = 78.5 in 2 base

7) Find the volume of shape. 12 m Area = 36.2 m 2 base

Volume = area x height Volume = 36.2 x 12 = m 3 12 m Area = 36.2 m 2 base

8) Find the volume of the triangular prism. 10ft 15ft 8ft

Area of base = 8 x 10 ÷ 2 = 40 ft 2 40 x 15 = 600 ft 3 10ft 15ft 8ft

9) Find the volume of the triangular prism. 8m 12m 6m

8m 12m 6m Area of base = 6 x 8 ÷ 2 = 24 ft 2 24 x 12 = 288 m 3

10) Find the volume of the triangular prism. 7 cm 11 cm 6cm

7 cm 11 cm 6cm Area of base = 6 x 7 ÷ 2 = 21 ft 2 21 x 11 = 231 m 3

11) Find the volume of the cylinder. 6 in 3 in

Area of base = 3 x 3 x 3.14 = in x 6 = in 3 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 km x 8 = 628 km 3

13) Find the volume of the cylinder. 11 m 8 m

11 m 8 m Area of base = 8 x 8 x 3.14 = m x 11 = m 3

THE END!