List of formulae 337
(v) Circle Area = πr
2 Circumference = 2πr
r
r
s
␪
Radian measure: 2π radians = 360 degrees
For a sector of circle:
arc length, s =
θ ◦
360
(2πr) = rθ
( θin rad)
shaded area =
θ ◦
360
(πr 2 ) =
1
2
r 2 θ
( θin rad)
Equation of a circle, centre at origin, radius r:
x
2
+ y
2
= r
2
Equation of a circle, centre at (a, b), radius r:
(x − a)
2
+ (y − b)
2
= r
2
Volumes and surface areas of regular
solids:
(i) Rectangular prism (or cuboid)
Volume = l × b × h
Surface area = 2(bh + hl + lb)
h
b
l
(ii) Cylinder
Volume = πr
2 h
Total surface area = 2πrh + 2πr
2
r
h
(iii) Pyramid
If area of base = A and
perpendicular height = h then:
Volume =
1
3
× A × h
h
Total surface area = sum of areas of triangles
forming sides + area of base
(iv) Cone
Volume =
1
3
πr
2 h
Curved Surface area = πrl
Total Surface area = πrl + πr
2
l
h
r
(v) Sphere
Volume =
4
3
πr
3
Surface area = 4πr
2
r