Degrees and Radians
2.
3.
π radians = 180°
180°
1 radian =
π
π
1° =
radians
180°
To convert from degrees to radians and from radians to degrees:
×
π
180°
Degree
Radian
×
180°
π
Conversion of Units
4.
Length
1 m = 100 cm
1 cm = 10 mm
Area
1 cm2 = 10 mm × 10 mm
= 100 mm2
2
1 m = 100 cm × 100 cm
= 10 000 cm2
Volume
1 cm3 = 10 mm × 10 mm × 10 mm
= 1000 mm3
1 m3 = 100 cm × 100 cm × 100 cm
= 1 000 000 cm3
1 litre = 1000 ml
= 1000 cm3
Mensuration
133
Volume and Surface Area of Solids
5.
Figure
Diagram
Formulae
Cuboid
h
Volume = l × b × h
Total surface area = 2(lb + lh + bh)
b
l
r
Cylinder
h
Volume = πr2h
Curved surface area = 2πrh
Total surface area = 2πrh + 2πr2
Volume
= Area of cross section × length
Total surface area
= Perimeter of the base × height
+ 2(base area)
Prism
h
Pyramid
Volume =
1
× base area × h
3
1 2
πr h
3
Curved surface area = πrl
Volume =
Cone
l
h
r
134
UNIT 2.5
(where l is the slant height)
Total surface area = πrl + πr2
Figure
Sphere
Diagram
Formulae
4 3
πr
3
Surface area = 4πr 2
r
Volume =
r
Volume =
Hemisphere
2 3
πr
3
Surface area = 2πr2 + πr2
= 3πr2
Example 3
(a) A sphere has a radius of 10 cm. Calculate the volume of the sphere.
(b) A cuboid has the same volume as the sphere in part (a). The length and
breadth of the cuboid are both 5 cm. Calculate the height of the cuboid.
Leave your answers in terms of π.
Solution
4π(10)3
3
4000 π
=
cm3
3
(b) Volume of cuboid = l × b × h
4000 π
=5×5×h
3
160π
h=
cm
3
(a) Volume =
Mensuration
135