# Tastey Tuesday! Your new Pi Day question is coming on the next slide…

## Presentation on theme: "Tastey Tuesday! Your new Pi Day question is coming on the next slide…"— Presentation transcript:

Tastey Tuesday! Your new Pi Day question is coming on the next slide…

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. Label your answer, be sure your name is on it, and ask yourself: did I answer the question being asked?

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 = 12 ft 4 ft 3 ft

When you measure circumference, you are also measuring length.
4 x 3.14 = 12.56cm 4 cm

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 x 5 x 3.14 = 78.5 sq. cm 5 cm

Volume is a measure of 3 dimensions: LENGTH, WIDTH, & HEIGHT

Imagine starting with a piece of rectangular paper.

The area of this rectangle is 12 square inches

Now, suppose that we “stacked” another piece of paper on top of this piece of paper.
4 in 3 in

4 in 3 in

4 in 3 in

4 in 3 in

4 in 3 in

Now we have 2 pieces of paper, each with an area of 12
Now we have 2 pieces of paper, each with an area of 12. So the volume is 24. 4 in 3 in

Let’s add another piece of paper to the stack.
4 in 3 in

4 in 3 in

4 in 3 in

4 in 3 in

4 in 3 in

4 in 3 in

Now we have 3 pieces of paper, each with an area of 12
Now we have 3 pieces of paper, each with an area of 12. So the volume is 36. 4 in 3 in

If we had 100 pieces of paper stacked on top of one another, what would the volume be?
4 in 3 in

4 x 3 x 100 = 1200 100 4 in 3 in

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 1 in 1 in

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

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

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

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

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

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

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

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

Suppose that the area of this rectangle is 12.
3 4

Suppose that this rectangle served as the base of a rectangular prism.

Suppose that the prism has a height of 2.

2

2

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

then the volume should be 24 cubic units.

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 8 cm 3 cm

The volume is 72 cm3. 3 x 8 x 3 3 cm 8 cm 3 cm

2) Find the volume of the prism.

The volume is 300 in3. 12 x 5 x 5 5 in 12 in 5 in

3) Find the volume of the prism.
base base Area = 20 ft2

Volume = area x height Volume = 20 x 2.5 = 50 ft3
base base Area = 20 ft2

4) Find the volume of the prism.
base base Area = 12 m2

Volume = area x height Volume = 12 x 14 = 168 m3
base base Area = 12 m2

5) Find the volume of the prism.
25 cm base base Area = 15 cm2

Volume = area x height Volume = 15 x 25 = 375 cm3
base base Area = 15 cm2

6) Find the volume of the cylinder.
base base 10 in Area = 78.5 in2

Volume = area x height Volume = 78.5 x 10 = 785 in3
base base 10 in Area = 78.5 in2

7) Find the volume of shape.
base base Area = 36.2 m2

Volume = area x height Volume = 36.2 x 12 = 434.4 m3
base base Area = 36.2 m2

8) Find the volume of the triangular prism.

Area of base = 8 x 10 ÷ 2 = 40 ft2 40 x 15 = 600 ft3

9) Find the volume of the triangular prism.

Area of base = 6 x 8 ÷ 2 = 24 ft2 24 x 12 = 288 m3 6m 12m 8m

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

Area of base = 6 x 7 ÷ 2 = 21 ft2 21 x 11 = 231 m3 6cm 11 cm 7 cm

11) Find the volume of the cylinder.

Area of base = 3 x 3 x 3.14 = 28.26 in2 28.26 x 6 = 169.56 in3

12) Find the volume of the cylinder.
5 km 8 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.

Area of base = 8 x 8 x 3.14 = m x 11 = m3 8 m 11 m

Homework: Complete Worksheet Practice A/ B/ C/ Problem Solving