Basic Engineering Mathematics, Fifth Edition

List of formulae 337

(v)Circle Area=πr^2 Circumference= 2 πr

r

r

s



Radian measure: 2πradians=360degrees

For a sector of circle:

arc length, s=

θ◦

360

( 2 πr)=rθ(θin rad)

shaded area=

θ◦

360

(πr^2 )=

1

2

r^2 θ(θin rad)

Equation of a circle, centre at origin, radiusr:

x^2 +y^2 =r^2

Equation of a circle, centre at (a,b),radiusr:

(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= 2 πrh+ 2 πr^2

r

h

(iii) Pyramid

If area of base=Aand

perpendicular height=hthen:

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= 4 πr^2

r