MEASUREMENT�

TERM 2

MRSTAV

MEASUREMENT

Determine, through investigation using a variety of tools and strategies, the relationship for calculating the circumference and the area of a circle, and generalise to develop the formula.

MRSTAV

CURRICULUM

MEASUREMENT

Solve problems involving the estimation and calculation of the circumference and area of a circle.

MRSTAV

CURRICULUM

Table of Contents

# Volume of a Cylinder M

Volume of a Cylinder

M

DO IT NOW

MRSTAV

Create two different cylinders from an 8^1/2 x11 paper, one rolled lengthwise, the other rolled widthwise

(do not worry about making a base)

Will the containers hold the same amount of popcorn?

MRSTAV

MRSTAV

WE NEED TO GO BACK IN TIME!

MRSTAV

MRSTAV

RADIUS

AREA

a = π x r²

a = πr²

MRSTAV

RADIUS

AREA

a = πr²

a =

(3.14159)

2²

a =

(3.14159)

4

a =

^12.566

Square units

MRSTAV

MRSTAV

RADIUS

AREA

a = π x r²

a = πr²

7cm

a =

(3.14)

7²

a =

(3.14)

49

a =

153.86

cm²

MRSTAV

SO NOW LET’S APPLY THAT TO FIND THE

VOLUME OF A CYLINDER

MRSTAV

WHAT IS THE VOLUME

WITH A HEIGHT OF “0”

How much Cream Soda could be in this pop can?

NONE!

Or ZERO

​

MRSTAV

WHAT IS THE VOLUME

WITH A HEIGHT OF “0”

height

AREA

v = πr²h

v =

(3.14)2²

x 0

v =

(3.14)4

x 0

v =

12.56

x 0

volume

v =

0

units³

CUBED

^(VOLUME)

v = πr² x h

MRSTAV

WHAT IS THE VOLUME

WITH A HEIGHT OF “1”

height

AREA

v = πr² x h

v =

(3.14)2²

x 1

v =

(3.14)4

x 1

v =

12.56

x 1

volume

v =

12.56

units³

CUBED

^(VOLUME)

MRSTAV

WHAT IS THE VOLUME

WITH A HEIGHT OF “2”

height

AREA

v = πr² x h

v =

(3.14)2²

x 2

v =

(3.14)4

x 2

v =

12.56

x 2

volume

v =

25.12

units³

CUBED

^(VOLUME)

MRSTAV

WHAT IS THE VOLUME

WITH A HEIGHT OF “3”

height

AREA

v = πr² x h

v =

(3.14)2²

x 3

v =

(3.14)4

x 3

v =

12.56

x 3

volume

v =

37.68

units³

CUBED

^(VOLUME)

MRSTAV

WHAT IS THE VOLUME

WITH A HEIGHT OF “9”

height

AREA

v = πr² x h

v =

(3.14)2²

x 9

v =

(3.14)4

x 9

v =

12.56

x 9

volume

v =

113.04

units³

CUBED

^(VOLUME)

1

2

3

4

5

6

7

8

9

MRSTAV

VOLUME OF A CYLINDER

v = πr² x h

MRSTAV

VOLUME OF A CYLINDER

v = πr²h

BUT THAT’S HARD TO REMEMBER

MRSTAV

VOLUME OF A CYLINDER

v = πr²h

BUT THAT’S HARD TO REMEMBER

height

AREA

volume

v = πr² x h

MRSTAV

TIME FOR

A RIDDLE!

(THIS RIDDLE WAS MADE BY A STUDENT)

MRSTAV

A Pizza has a radius of ‘z’ and a height of “a”

​

Using these variables, what is the volume of a Pizza?

MRSTAV

A Pizza has a radius of ‘z’ and a height of “a”

​

Using these variables, what is the volume of a Pizza?

v =

π

z²

a

v =

Pi

x z

x z

x a

v =

Pi

z

z

a

v = πr²h

MRSTAV

VOLUME OF A CYLINDER

v = πr²h

v = Pizza

MR. STAV

LIKES PIZZA!

OR

MRSTAV

A can of Pringles has a diameter of 7cm and a height of 24cm.

What is the volume of a can of Pringles?

TRY IT

MRSTAV

A can of Pringles has a diameter of 7cm and a height of 24cm.

What is the volume of a can of Pringles?

TRY IT

Radius = 7 ÷ 2 =

3.5cm

v = Pizza

v = πr²h

v = (3.14159)(3.5²)(24)

v = (3.14159)(12.25)(24)

v = 923.62746cm³

​

​

NOT A RADIUS

MRSTAV

TRY IT

a)

b)

c)

d)

8 mm

20 mm

13.6 km

14.1 km

6.4 m

9.9 m

6.3 cm

9.2 cm

MRSTAV

TRY IT

a)

b)

c)

d)

8 mm

20 mm

v = πr²h

v = (3.14159)(6.3²)(9.2)

v = (3.14159)(39.69)(9.2)

v = 1 147.14cm³

​

13.6 km

14.1 km

v = πr²h

v = (3.14159)(4²)(20)

v = (3.14159)(16)(20)

v = 1 005.30mm³

​

v = πr²h

v = (3.14159)(6.8²)(14.1)

v = (3.14159)(46.24)(14.1)

v = 2 048.26 km³

​

v = πr²h

v = (3.14159)(6.4²)(9.9)

v = (3.14159)(40.96)(9.9)

v = 1 273.92m³

​

6.4 m

9.9 m

6.3 cm

9.2 cm

MRSTAV

MRSTAV

1. Players take turns tossing their bean bag trying to get 1 Pepperoni and 1 bacon

​

• Once a player gets 1 of each, they will plug the dimensions into the formula and solve for volume.

​

• If solved correctly, the player gets 5 points. If incorrect, the opponent can steal for 3 points.

GAME: “PIZZA TOSS”

v = Pizza

v = πr²h

v = (3.14159)(2²)(4.3)

v = (3.14159)(4)(4.3)

v = 50.03 cm³

MRSTAV

TECH

INDEPENDENT

WORK

MATH GAME

MATH

JOURNAL

bit.ly/stavmathjournal

1. joinkh.com
2. Class Code: flip4389

MRSTAV

>>

>>

>>

>>

CENTRES

GUIDED

WITH STAV

1 2 3 4 5

TECH

INDEPENDENT

WORK

MATH GAME

MATH

JOURNAL

1. joinkh.com
2. Class Code: flip4389

bit.ly/stavmathjournal

MRSTAV

>>

>>

>>

>>

CENTRES

GUIDED

WITH STAV

1 2 3 4 5

1

3

2

5

1

2

Full

12.2m

550cm

How much more can these beakers hold?

MRSTAV

A cylindrical beaker with a base diameter of 9 cm has a height of 38.5 cm. Assuming that water expands 10% when it freezes, determine the depth to which the container can be filled so that when the contents freeze, the ice does not go above the top of the container.

MRSTAV

MEASUREMENT

• Measure the circumference, radius and diameter of circular objects using concrete materials.
• Determine, through investigation using a variety of tools and strategies, the relationship for calculating the circumference and the area of a circle, and generalise to develop the formula.
• Solve problems involving the estimation and calculation of the circumference and area of a circle.

MRSTAV

CURRICULUM