Basic Engineering Mathematics, Fifth Edition

30 Basic Engineering Mathematics

Problem 26. The volumeVcm^3 of a right

circular cone is given byV=

1

3

πr^2 h. Given that

radiusr= 2 .45cm and heighth= 18 .7cm,findthe

volume, correct to 4 significant figures

V=

1

3

πr^2 h=

1

3

π( 2. 45 )^2 ( 18. 7 )

=

1

3

×π× 2. 452 × 18. 7

= 117. 544521 ...

Hence,volume,V = 117 .5cm^3 , correct to 4 signifi-

cant figures.

Problem 27. ForceFnewtons is given by the

formulaF=

Gm 1 m 2

d^2

,wherem 1 andm 2 are

masses,dtheir distance apart andGis a constant.

Find the value of the force given that

G= 6. 67 × 10 −^11 ,m 1 = 7 .36,m 2 = 15 .5and

d= 22 .6. Express the answer in standard form,

correct to 3 significant figures

F=

Gm 1 m 2

d^2

=

( 6. 67 × 10 −^11 )( 7. 36 )( 15. 5 )

( 22. 6 )^2

=

( 6. 67 )( 7. 36 )( 15. 5 )

( 1011 )( 510. 76 )

=

1. 490

1011

Hence,forceF= 1. 49 × 10 −^11 newtons, correct to

3 significant figures.

Problem 28. The time of swing,tseconds, of a

simple pendulum is given byt= 2 π

√

l

g

Determine the time, correct to 3 decimal places,

given thatl= 12 .9andg= 9. 81

t= 2 π

√

l

g

=( 2 π)

√

12. 9

9. 81

= 7. 20510343 ...

Hence,timet= 7 .205seconds,correct to 3 decimal

places.

Problem 29. Resistance,R, varies with

temperature according to the formula

R=R 0 ( 1 +αt). EvaluateR, correct to 3 significant

figures, givenR 0 = 14 .59,α= 0 .0043 andt= 80

R=R 0 ( 1 +αt)= 14 .59[1+( 0. 0043 )( 80 )]

= 14. 59 ( 1 + 0. 344 )

= 14. 59 ( 1. 344 )

Hence,resistance,R= 19. 6 , correct to 3 significant

figures.

Problem 30. The current,Iamperes, in an a.c.

circuit is given byI=

V

√

(R^2 +X^2 )

.Evaluatethe

current, correct to 2 decimal places, when

V=250V,R= 25. 0 andX= 18. 0 .

I=

V

√

(R^2 +X^2 )

=

250

√(

25. 02 + 18. 02

)=^8.^11534341 ...

Hence, current,I= 8. 12 A, correct to 2 decimal

places.

Now try the following Practice Exercise

PracticeExercise 20 Evaluation of

formulae (answers on page 341)

1. Find the total cost of 37 calculators cost-
   ing £12.65each and 19 drawing sets costing
   £6.38 each.


2. Power=

force×distance

time

. Find the power

when a force of 3760N raises an object a

distance of 4.73m in 35s.

3. The potential difference,Vvolts, available
   at battery terminals is given byV=E−Ir.
   EvaluateV whenE= 5 .62,I= 0 .70 and
   R= 4. 30


4. Given forceF=

1

2

m(v^2 −u^2 ),findFwhen

m= 18. 3 ,v= 12 .7andu= 8. 24

5. The currentIamperes flowing in a number
   of cells is given byI=

nE

R+nr

.Evaluatethe

current whenn=36,E= 2 .20, R= 2. 80

andr= 0. 50

6. The time,t seconds, of oscillation for a
   simple pendulum is given byt= 2 π

√

l

g

.

Determine the time whenl= 54 .32 and

g= 9. 81