Units Of Measurement And Applications Worksheet Page 20
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44WORKED EXAMPLE 7
The length and breadth of a rectangle were measured to be 8 cm and 6 cm
respectively.
6 cm
a
Calculate the area using the measurements given.
b
Find the lower and upper limits of the true area.
c
Hence, fi nd the maximum error in the answer to part a.
8 cm
Solve
Think
Apply
Area = 8 × 6 = 48 cm
2
a
Area (using given measurements)
Calculate the area using the
= l × b = 48 cm
2
measured length and breadth.
Determine the lower and
Now 7.5 cm ⩽ length < 8.5 cm
b
The GPE of each measurement
and 5.5 cm ⩽ breadth < 6.5 cm.
upper limits of each given
is 0.5 cm. Hence, the length lies
measurement.
Hence, 7.5 × 5.5 cm
⩽ area
2
between 7.5 cm and 8.5 cm and
< 8.5 × 6.5 cm
Calculate the area using the
the breadth lies between 5.5 cm
2
.
lower limits of the length and
and 6.5 cm.
Thus
breadth, and calculate the area
⩽ area < 55.25 cm
Lower limit of area
2
2
41.25 cm
.
= 7.5 × 5.5 = 41.25 cm
2
using the upper limits of the
Upper limit of area
length and breadth.
= 8.5 × 6.5 = 55.25 cm
2
Find the diff erence between
the area calculated using the
c
48 − 41.25 = 6.75 cm
Maximum error = area
2
given measurements and the
48 − 55.25 = −7.25 cm
2
(using given measurements)
area using the lower (or upper)
− lower limit of area
Maximum error = 7.25 cm
2
limit of each measurement.
(or upper limit of area).
19
T he length and breadth of a rectangle are measured to be 7 cm and 4 cm respectively. Complete the following.
Using the given measurements, area = ____ × ____ cm
= ____ cm
a
2
2
Now 6.5 cm ⩽ length < ____ cm and ____ cm ⩽ breadth < 4.5 cm
b
Hence, lower limit of area = 6.5 × 3.5 cm
= ____ cm
2
2
upper limit of area = ____ × ____ cm
= ____ cm
2
2
⩽ area < ____ cm
2
2
Thus ____ cm
____ − lower limit of area = ____ cm
c
2
____ − upper limit of area = ____ cm
2
∴ Maximum error = ± ____ cm
2
20
A rectangular room was measured
to be 5 m long by 3 m wide.
3 m
a
Calculate the area of the room
using these measurements.
5 m
b
Find the lower and upper limits
of the true length and width.
c
What are the lower and upper limits of the true area?
d
Find the maximum error in the answer to part a.
21
Repeat question 20 for a room 5.4 m long by 3.2 m wide.
54
Insight Mathematics General 11
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