Basic Engineering Mathematics, Fifth Edition

Volumes of common solids 243

Total surface area=area of each end+area of three
sides.

In triangleABC, AC^2 =AB^2 +BC^2

from which, AC=

√

AB^2 +BC^2 =

√

62 + 82

=10cm

Hence, total surface area

= 2

(

1

2

bh

)

+(AC× 40 )+(BC× 40 )+(AB× 40 )

=( 8 × 6 )+( 10 × 40 )+( 8 × 40 )+( 6 × 40 )

= 48 + 400 + 320 + 240

i.e. total surface area=1008cm^2

Problem 8. Calculate the volume and total

surface area of the solid prism shown in Figure 27.7

15cm

5cm

5cm

5cm

4cm

11cm

Figure 27.7

The solid shown in Figure 27.7 is atrapezoidal prism.

Volume of prism=cross-sectional area×height

=

1

2

( 11 + 5 ) 4 × 15 = 32 × 15

=480cm^3

Surface area of prism

=sum of two trapeziums+4 rectangles

=( 2 × 32 )+( 5 × 15 )+( 11 × 15 )+ 2 ( 5 × 15 )

= 64 + 75 + 165 + 150 =454cm^2

Now try the following Practice Exercise

PracticeExercise 105 Volumes and surface

areasof commonshapes (answerson

page 351)

1. Change a volume of 1200000cm^3 to cubic
   metres.


2. Change a volume of 5000mm^3 to cubic
   centimetres.


3. A metal cube has a surface area of 24cm^2.
   Determine its volume.


4. A rectangular block of wood has dimensions
   of 40mm by 12mm by 8mm. Determine
   (a) its volume, in cubic millimetres
   (b) its total surface area in square millime-
   tres.


5. Determinethecapacity,in litres,ofafish tank
   measuring90cmby60cmby1.8m, given
   1litre=1000cm^3.


6. A rectangular block of metal has dimensions
   of 40mm by 25mm by 15mm. Determine its
   volumeincm^3. Findalso its mass if themetal
   has a density of 9g/cm^3.


7. Determine the maximum capacity, in litres,
   of a fish tank measuring 50cm by 40cm by
   2 .5m(1litre=1000cm^3 ).


8. Determine how many cubic metres of con-
   crete are required for a 120m long path,
   150mm wide and 80mm deep.


9. A cylinder has a diameter 30mm and height
   50mm. Calculate
   (a) its volume in cubic centimetres, correct
   to 1 decimal place
   (b) the total surface area in square centime-
   tres, correct to 1 decimal place.


10. Find (a) the volume and (b) the total sur-
    face area of a right-angled triangular prism
    of length 80cm and whose triangular end
    has a base of 12cm and perpendicular
    height 5cm.


11. A steel ingot whose volume is 2m^2 is rolled
    out into a plate which is 30mm thick and
    1 .80m wide. Calculate the lengthof the plate
    in metres.