Volume

Learning Goals

By the end of the lesson I will be able to:

• Calculate the volume of prisms pyramids cones and spheres

How much to fill?

How much paint would it take to cover:

How much paint would it take to fill:

8cm

10 cm

A = (b x h) / 2

= (8 x 10) / 2

= (80) / 2

= 40 cm²

​

8cm

10 cm

50cm

V = 40 cm² x 50cm

= 2000 cm³

​

How much to fill?

How much paint would it take to cover:

How much paint would it take to fill:

A = πr²

= π(5)²

= π(25)

= 78.54 cm²

​

V = 78.54 cm² x 20cm

= 1570.8 cm³

​

5cm

5cm

20cm

How much to fill?

How much paint would it take to cover:

How much paint would it take to fill:

A = l x w

= 3 x 7

= 21 m²

​

V = 21 m² x 6m

= 126 m³

​

7 m

3 m

7 m

3 m

6 m

Prisms

Each of the previous 3 examples showed us how to find the volume of any prism (or cylinder).

• Find the area of the prism base (circle, triangle or rectangle)
• Multiply by the height

​

How much to fill?

How much paint would it take to cover:

How much paint would it take to fill:

A = l x w

= 4 x 4

= 16 cm²

​

V = 16 m² x 6m

= 96 m³

Incorrect!

​

The volume of any pyramid is ⅓ the volume of the same prism!

​

V = (16 m² x 6m) / 3

= 32 m³

4 cm

4 cm

4 cm

4 cm

6 cm

How much to fill?

How much paint would it take to cover:

How much paint would it take to fill:

A = πr²

= π(6)²

= π(36)

= 113.1 cm²

​

V = (113.1 cm² x 10 cm) / 3

= 377 cm³

6 cm

10 cm

6 cm

Formula Recap

Any Prism

Any Pyramid

V = A_base x height

V = A_base x height

3

What about spheres?

V = 4 π r³

3