Question

A rectangular plate has a length of (21.7 ± 0.2) cm and a width of (8.2 ± 0.1) cm. Calculate the area of the plate, including its uncertainty

Answer 1

Answer:

(177.94 ± 3.81) cm^2

Explanation:

l + Δl = 21.7 ± 0.2 cm

b + Δb = 8.2 ± 0.1 cm

Area, A = l x b = 21.7 x 8.2 = 177.94 cm^2

Now use error propagation

$\frac{\Delta A}{A}=\frac{\Delta l}{l}+\frac{\Delta b}{b}$

$\frac{\Delta A}{A}=\frac{0.2}{21.7}+\frac{0.1}{8.2}$

$\Delta A=177.94 \times \left ( 0.0092 + 0.0122 \right )=3.81$

So, the area with the error limits is written as

A + ΔA = (177.94 ± 3.81) cm^2