Question

If length and breadth of a plate are
(40+0.2) cm and (30+0.1)cm, the absolute
error in measurement of area is
2) 8 cm? 3) 9 cm? 4) 7 cm
1) 10cm?​

Answer 1

$\large{\underline{\underline{\mathfrak{Answer :}}}}$

• Error in measurement of Area of rectangle is ± 10 cm²

$\underline{\underline{\mathfrak{Step - By -Step -Explanation \: :}}}$

• Length (L) = (40 ± 0.2) cm
• Breadth (B) = (30 ± 0.1) cm

First we will find area of rectangle without including error limits.

$\longrightarrow \sf{Area \: = \: Length \: \times \: Breadth} \\ \\ \longrightarrow \sf{A \: = \: 40 \: \times \: 30} \\ \\ \longrightarrow \sf{A \: = \: 1200} \\ \\ \underline{\sf{\therefore \: Area \: of \: rectangle \: is \: 1200 \: cm^2}}$

______________________________

Now, we have to calculate error in measurement of area :

For this use error in Multiplication Case :

$\dashrightarrow {\boxed{\sf{\dfrac{\Delta A}{A} \: = \: \dfrac{\Delta L}{L} \: + \: \dfrac{\Delta B}{B}}}} \\ \\ \dashrightarrow \tt{\dfrac{\Delta A}{1200} \: = \: \dfrac{0.2}{40} \: + \: \dfrac{0.1}{30}} \\ \\ \dashrightarrow \tt{\Delta A \: = \: 1200 \: \times \: \bigg( \dfrac{0.2 \: \times \: 30 \: + \: 0.1 \: \times \: 40}{1200} \bigg)} \\ \\ \dashrightarrow \tt{\Delta A \: = \: 0.2 \: \times \: 30 \: + \: 0.1 \: \times \: 40} \\ \\ \dashrightarrow \tt{\Delta A \: = \: 6 \: + \: 4} \\ \\ \dashrightarrow \tt{\Delta A \: = \: 10} \\ \\ \underline{\sf{\therefore \: Error \: in \: measurement \: of \: area \: is \: \pm \: 10 \: cm^2}}$

Answer 2

Given :

• Length = (40 ± 0.2 ) cm
• Breadth = (30 ± 0.1) cm

To find :

• Absolute error in measurement

Solution:

Area of the plate (A) = length × breadth

= 40 × 30

= 1200 cm²

We know that

$\boxed{\rm \dfrac{\Delta A}{A} = \dfrac{\Delta L}{L} + \dfrac{\Delta B}{B}}$

$\rm \Delta A = A \times \dfrac{\Delta L}{L} + \dfrac{\Delta B}{B}$

$= 1200 \times (\frac{0.2}{40} + \frac{0.1}{30} )$

$= 1200( \frac{0.2 \times 30 + 0.1 \times 40}{1200} )$

$= 1200( \frac{6 + 4}{1200} )$

$= 1200 \times \frac{10}{1200}$

$= 10$

Hence , the absolute error in measurement of area is 10 cm² .

$\boxed{ \large\rm \orange{area} \: = \pink{1200} \pm \red{10} \: \purple{ {cm}^{2} }}$