Question

The side of a square is measured to be 10 ft with a possible error of ±0.1 ft. Use linear approximation or differentials to estimate the error in the calculated area. Include units in your answer

Answer 1

Answer:

The error in the calculation of the area will be 2 square feet.

Step-by-step explanation:

Let the actual length of the square is L ft.  

So, actual area A = L² ......... (1)

Now, if there is an error in measuring length is ΔL, then  

(A + ΔA) = (L + ΔL)² {Since if there is an error in length by ΔL, then there will be an error in the calculation of area by ΔA}

⇒ A + ΔA = L² + 2×L×ΔL + (ΔL)²

Now, by linear approximation, neglect the term (ΔL)² as it will be very small.

So, A + ΔA = A + 2×L×ΔL {Since A = L²}

⇒ ΔA = 2×L×ΔL .......... (2)

Now, given that  L = 10 ft and ΔL = 0.1 ft.

Hence, ΔA = 2× 10× 0.1 = 2 sq. ft.

Therefore, the error in the calculation of the area will be 2 square feet. (Answer)