Find the area of a rectangular room measuring 9.7 m by 14.5 m. Express your answ

Question

Find the area of a rectangular room measuring 9.7 m by 14.5 m. Express your answer with the correct number of significant figures. Answers should be in the format of Structured Problem Solving.

Here is an example of Structured Problem Solving:
Key Idea: Write down a short statement of the physical principle which you think is the most relevant to solving the problem. Describe the elements of the problem which indicated that this physical principle might be applicable.

Stock of Data: Make a list of the numerical data you are given in the problem description. Be sure to include units. List quantities you are asked to calculate with trailing question marks. This step may include a diagram indicating your understanding of the problem.

I.D. Equation: Choose an equation which reflects both the key idea of your problem and information from your stock of data. You may need more than one equation.

Solve: If the equation or equations you have chosen are not already solved for you unknown then do the algebra to accomplish this now. Be sure to show enough detail in each step so that a reader can follow your work.

Substitute in Numerical Data: Once you have an analytic solution, substitute numerical values into the analytic solution to obtain the final answer.

Sanity Check: Answer the question. “Does this answer make sense in light of the rest of the knowledge I possess?” The sanity check could include a back of the envelope calculation done with a single significant digit or a unit analysis of the final answer.

Example: 20 mg particle is placed in a downward electric field of 2000 N/C. How many excess electrons must be placed on the particle for the electric and gravitational forces to balance?

Key Idea: Equilibrium and Coulombs Law – The problem statement talks about a balance of forces (equilibrium) and forces on charges (Coulomb’s law).

Stock of Data: mass = 2.0 x 10-5 kg qelectron = 1.602 x 10-19 C g = 9.81 m/s^2 E = 2000 N/C n = quantity to be solved for

ID Equation: Use F1 + F2 = 0 for the equilibrium condition, where F1 = mass * g and F2 = n * qelectron * E.

Solve: F1 + F2 = 0 becomes mass * g + n * qelectron E = 0 or q = - (mass * g) / (E * qelectron) and so n = (mass * g) / (qelectron * E)

Substitute in Data: n = - (2.0 x 10-5 kg) (9.81 m/s^2) / (2000 N/C * -1.602 x 10-19 C) n = 6.12 x 1011 electrons

Sanity Check: This is an enormous number and so I will content myself with checking the units to make sure SI units cancel and the answer is a pure number.

Sanity check 1: Unit analysis n = - (2.0 x 10-5 kg) (9.81 m/s^2) / (2000 N/C * -1.602 x 10-19 C) reduced to units and recognize (kg m/s2 = N)
[n] = [kg * m/s2 * C/N * 1/ C]
[n]= [kg m/s2 * 1/N] which is unit less as is required for a pure number.

Sanity check 2: Estimation of magnitude (~ is "about" , ~= is "about equal to") n ~ = (2.0 x 10-5) (~10 ) / (2.0 * 103 * ~ 1.5 *10-19) n ~= 2.0 /2.0 / 1.5 x 10(-5 +1 -3 +19) ~= 1/1.5 x 1012 since 1.5 = 3/2 therefore 1/1.5 equals 2/3 or about 0.6 n ~= 0.6 x 1012 .... n is roughly 6 * 1011

Explanation / Answer

Area of rectangle=length*breadth

Area=9.7*14.5=140.65

But length and breadth are upto 1 place o decimal so

Area=140.7 m^2

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