Basic Engineering Mathematics, Fifth Edition

Volumes of common solids 241

(a) Volume of oil tank=volume of cube

= 1 .5m× 1 .5m× 1 .5m

= 1. 53 m^3 =3.375m^3

1m^3 =100cm×100cm×100cm= 106 cm^3.

Hence,

volume of tank= 3. 375 × 106 cm^3

1litre=1000cm^3 , henceoil tank capacity

=

3. 375 × 106

1000

litres=3375litres

(b) Surface area of one side= 1 .5m× 1 .5m
= 2 .25m^2.
A cube has six identical sides, hence

total surface area of oil tank= 6 × 2. 25

= 13 .5m^2

Problem 3. A water tank is the shape of a

rectangular prism having length 2m, breadth 75cm

and height 500mm. Determine the capacity of the

tank in (a) m^3 (b) cm^3 (c) litres

Capacity means volume; when dealing with liquids, the
word capacity is usually used.
The water tank is similar in shape to that in Figure 27.1,
withl=2m,b=75cm andh=500mm.

(a) Capacity of water tank=l×b×h.To usethis for-

mula, all dimensionsmustbe in the same units.

Thus,l=2m,b= 0 .75m andh= 0 .5m (since

1m=100cm=1000mm). Hence,

capacity of tank= 2 × 0. 75 × 0. 5 =0.75m^3

(b) 1m^3 =1m×1m×1m
=100cm×100cm×100cm
i.e.,1m^3 = 1000000 =10^6 cm^3. Hence,
capacity= 0 .75m^3 = 0. 75 × 106 cm^3

=750000cm^3

(c) 1litre=1000cm^3. Hence,

750000cm^3 =

750 , 000

1000

=750litres

27.2.2 Cylinders

A cylinder is a circular prism. A cylinder of radiusrand
heighthis shown in Figure 27.2.

h

r

Figure 27.2

Volume=πr^2 h

Curved surface area= 2 πrh

Total surface area= 2 πrh+ 2 πr^2

Total surface area means the curved surface area plus

the area of the two circular ends.

Problem 4. A solid cylinder has a base diameter

of 12cm and a perpendicular height of 20cm.

Calculate (a) the volume and (b) the total surface

area

(a) Volume=πr^2 h=π×

(

12

2

) 2

× 20

= 720 π=2262cm^3

(b) Total surface area

= 2 πrh+ 2 πr^2

=( 2 ×π× 6 × 20 )+( 2 ×π× 62 )

= 240 π+ 72 π= 312 π=980cm^2

Problem 5. A copper pipe has the dimensions

shown in Figure 27.3. Calculate the volume of

copper in the pipe, in cubic metres.

2.5m

12cm

25cm

Figure 27.3