Using a calculator 29
Problem 22. Velocity v is given by v = u + at . If
u = 9.54 m/s, a = 3.67 m/s 2 and t = 7.82 s, find v,
correct to 3 significant figures
v = u + at = 9.54 + 3.67 × 7.82
= 9.54 + 28.6994 = 38.2394
Hence, velocity v = 38.2 m/s, correct to 3 significant
figures.
Problem 23. The area, A, of a circle is given by
A = πr 2 . Determine the area correct to 2 decimal
places, given radius r = 5.23 m
A = πr
2
= π(5.23)
2
= π(27.3529)
Hence, area, A = 85.93 m 2 , correct to 2 decimal
places.
Problem 24. Density =
mass
volume
. Find the density
when the mass is 6.45 kg and the volume is
300 × 10 −6 cm 3
Density =
mass
volume
=
6.45 kg
300 × 10 −6 m 3 = 21500 kg/m
3
Problem 25. The power, P watts, dissipated in an
electrical circuit is given by the formula P =
V 2
R
.
Evaluate the power, correct to 4 significant figures,
given that V = 230 V and R = 35.63
P =
V
2
R
=
(230)
2
35.63
=
52900
35.63
= 1484.70390 ...
Press ENG and 1.48470390 ... × 10 3 appears on the
screen.
Hence, power, P = 1485 W or 1.485 kW correct to 4
significant figures.
Now try the following Practice Exercise
Practice Exercise 19 Evaluation of
formulae (answers on page 341)
1. The area A of a rectangle is given by the
formula A = lb. Evaluate the area when
l = 12.4 cm and b = 5.37 cm.
2. The circumference C of a circle is given by
the formula C = 2πr. Determine the circumference given r = 8.40 mm.
3. A formula used in connection with gases
is R =
PV
T
. Evaluate R when P = 1500,
V = 5 and T = 200.
4. The velocity of a body is given by v = u + at .
The initial velocity u is measured when time
t is 15 seconds and found to be 12 m/s. If the
acceleration a is 9.81 m/s
2 calculate the final
velocity v.
5. Calculate the current I in an electrical circuit,
where I = V /R amperes when the voltage V
is measured and found to be 7.2 V and the
resistance R is 17.7 .
6. Find the distance s, given that s =
1
2
gt 2
when time t = 0.032 seconds and acceleration due to gravity g = 9.81 m/s
2 . Give the
answer in millimetres.
7. The energy stored in a capacitor is given
by E =
1
2
CV 2 joules. Determine the energy
when capacitance C = 5 × 10 −6 farads and
voltage V = 240 V.
8. Find the area A of a triangle, given A =
1
2
bh,
when the base length l is 23.42 m and the
height h is 53.7 m.
9. Resistance R 2 is given by R 2 = R 1 (1 + αt ).
Find R 2 , correct to 4 significant figures, when
R 1 = 220, α = 0.00027 and t = 75.6
10. Density =
mass
volume
. Find the density when
the mass is 2.462 kg and the volume is
173 cm 3 . Give the answer in units of kg/m
3 .
11. Velocity = frequency × wavelength. Find
the velocity when the frequency is 1825 Hz
and the wavelength is 0.154 m.
12. Evaluate resistance R T , given
1
R T
=
1
R 1
+
1
R 2
+
1
R 3
when R 1 = 5.5 ,
R 2 = 7.42 and R 3 = 12.6 .
Here are some further practical examples. Again, check
with your calculator that you agree with the working
and answers.
Problem 22. Velocity v is given by v = u + at . If
u = 9.54 m/s, a = 3.67 m/s 2 and t = 7.82 s, find v,
correct to 3 significant figures
v = u + at = 9.54 + 3.67 × 7.82
= 9.54 + 28.6994 = 38.2394
Hence, velocity v = 38.2 m/s, correct to 3 significant
figures.
Problem 23. The area, A, of a circle is given by
A = πr 2 . Determine the area correct to 2 decimal
places, given radius r = 5.23 m
A = πr
2
= π(5.23)
2
= π(27.3529)
Hence, area, A = 85.93 m 2 , correct to 2 decimal
places.
Problem 24. Density =
mass
volume
. Find the density
when the mass is 6.45 kg and the volume is
300 × 10 −6 cm 3
Density =
mass
volume
=
6.45 kg
300 × 10 −6 m 3 = 21500 kg/m
3
Problem 25. The power, P watts, dissipated in an
electrical circuit is given by the formula P =
V 2
R
.
Evaluate the power, correct to 4 significant figures,
given that V = 230 V and R = 35.63
P =
V
2
R
=
(230)
2
35.63
=
52900
35.63
= 1484.70390 ...
Press ENG and 1.48470390 ... × 10 3 appears on the
screen.
Hence, power, P = 1485 W or 1.485 kW correct to 4
significant figures.
Now try the following Practice Exercise
Practice Exercise 19 Evaluation of
formulae (answers on page 341)
1. The area A of a rectangle is given by the
formula A = lb. Evaluate the area when
l = 12.4 cm and b = 5.37 cm.
2. The circumference C of a circle is given by
the formula C = 2πr. Determine the circumference given r = 8.40 mm.
3. A formula used in connection with gases
is R =
PV
T
. Evaluate R when P = 1500,
V = 5 and T = 200.
4. The velocity of a body is given by v = u + at .
The initial velocity u is measured when time
t is 15 seconds and found to be 12 m/s. If the
acceleration a is 9.81 m/s
2 calculate the final
velocity v.
5. Calculate the current I in an electrical circuit,
where I = V /R amperes when the voltage V
is measured and found to be 7.2 V and the
resistance R is 17.7 .
6. Find the distance s, given that s =
1
2
gt 2
when time t = 0.032 seconds and acceleration due to gravity g = 9.81 m/s
2 . Give the
answer in millimetres.
7. The energy stored in a capacitor is given
by E =
1
2
CV 2 joules. Determine the energy
when capacitance C = 5 × 10 −6 farads and
voltage V = 240 V.
8. Find the area A of a triangle, given A =
1
2
bh,
when the base length l is 23.42 m and the
height h is 53.7 m.
9. Resistance R 2 is given by R 2 = R 1 (1 + αt ).
Find R 2 , correct to 4 significant figures, when
R 1 = 220, α = 0.00027 and t = 75.6
10. Density =
mass
volume
. Find the density when
the mass is 2.462 kg and the volume is
173 cm 3 . Give the answer in units of kg/m
3 .
11. Velocity = frequency × wavelength. Find
the velocity when the frequency is 1825 Hz
and the wavelength is 0.154 m.
12. Evaluate resistance R T , given
1
R T
=
1
R 1
+
1
R 2
+
1
R 3
when R 1 = 5.5 ,
R 2 = 7.42 and R 3 = 12.6 .
Here are some further practical examples. Again, check
with your calculator that you agree with the working
and answers.