Shape and Space

1
Shape and Space

• Volume
• Level 7

2
A. Cubes.
1 cm3
Base area
height
5 cm
Base area 25 cm2
length
width
5 cm
4 cm
length
(base area)
( 25 ) 4
Volume of a prism height
100 cm3
width
3
A. Cubes.
Base area
Will the volume remain the same?
Base area 5 4 20 cm2 Volume 20 5 100
cm3
4
Revision of area
Worth remembering
a
a
Area of trapezium
h
h
½ (a b)h
b
b
Area of triangle
h
h
½ bh
b
b
5
Volume of prisms.
Trapezium-based prism.
height
A The cross-section remains constant through the
length of the prism.
length
Base area
Why that side?
6
Volume of prisms.
3cm
Trapezium-based prism.
3cm
3
4cm
4cm
4
6cm
10cm
6cm
6
Trapezium ½ ( a b ) h
Base area ½ ( a b ) h
( )
( )
( )
½ (9)(4)
18 cm2
7
Volume of prisms.
3cm
Trapezium-based prism.
3cm
3
4cm
4cm
4
6cm
10cm
10
6cm
6
Base area 18 cm2
18
Volume of prism base area length
( )
( )
180 cm3
8
Volume of prisms.
Triangle-based prism
height
4 cm
Base area
length
8 cm
base
6 cm
Area of triangle ½ b h
( )
( )
4 cm
4
12 cm2
6 cm
6
9
Volume of prisms.
height
4 cm
length
8 cm
8
base
6 cm
Area of base 12 cm2
12
Volume of Prism base area length
( )
( )
96 cm3
10
Volume of prisms.
length
Base area
length
Base area
Worth remembering
Volume of a prism base area length
11
B. Volume of a cylinder.
The cylinder is a special kind of prism.
Is the cylinder another prism?
12
B. Volume of a cylinder.
Base area
Volume of cylinder base area length
length
The base of a cylinder is a circle.
Area of a circle pr2
r
Worth remembering
13
Calculator will be required.

• Calculate the volume of the cylinder below

Radius 5 cm, Length 10 cm.
5 cm
(use the p key or let p 3.14)
10 cm
Base area p r2
p (5)2
78.53981634 cm2
Round off
78.5 cm2
Volume of cylinder 78.5 10
785 cm3