NOT TO
SCALE
hcm
18.6 cm
8.2 cm
30.6 cm
102 cm
16.4 cm
Find the value of h.

Error in product of quantities: Suppose x=a×b
Let Δa=absolute error in measurement of a,
Δb=absolute error in measurement of b,
Δx=absolute error in calculation of x, i.e. product of a and b.
The maximum fractional error in x is
x
Δx

=±(
a
Δa

+
b
Δb

)
Percentage error in the value of x=(Percentage error in value of a)+(Percentage error in value of b)
According to the problem, length l=(16.2±0.1)cm

Breadth b=(10.1±0.1)cm

Area A=l×b=(16.2cm)×(10.1cm)=163.62cm
2

As per the rule area will have only three significant figures and error will have only one significant figure.Rounding off we get,area A=164cm
2

If ΔA is error in the area, then relative error is calculated as
A
δ4

.

A
Δ4

=
l
Δl

+
b
Δb

=
16.2cm
0.1cm

+
10.1cm
0.1cm


=
16.2×10.1
1.01+1.62

=
163.62
2.63


⇒ΔA=A×
163.62
2.63

cm
2
=162.62×
163.62
2.63

=2.63cm
2

ΔA=3cm
2
(By rounding off to one significant figure)

Area, A=A±ΔA(164±3)cm
2

The correct answer is: 2