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

(177.94 ± 3.81) cm^2

Step-by-step 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

`(\Delta A)/(A)=(\Delta l)/(l)+(\Delta b)/(b)`

`(\Delta A)/(A)=(0.2)/(21.7)+(0.1)/(8.2)`

`\Delta A=177.94 * \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