if the length and the breadth of a thin rectangular sheet are measured in 16.2 cm 10.1cm respectively .find maximum percentage error in calculated area
Answers
Answer:
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