Q27PE - College Physics (Urone)

Question

The length and width of a rectangular room are measured to be \({\bf{3}}.{\bf{955}}{\rm{ }} \pm {\rm{ }}{\bf{0}}.{\bf{005m}}\) and \({\bf{3}}.{\bf{050}}{\rm{ }} \pm {\rm{ }}{\bf{0}}.{\bf{005m}}\). Calculate the area of the room and its uncertainty in square meters.

Step-by-Step Solution

Answer

The area of this room is \(12.062{\rm{ }}{m^2}\).

Step 1: Definition of area

The area of the room is defined by length multiplied by width.

Given data:

Consider the given data as below.

Length of the room, \(L = 3.955 \pm 0.005{\rm{ }}m\)

Width of the room, \(W = 3.050 \pm 0.005{\rm{ }}m\)

 

Step 2: Calculating area of the room

Area id defines as below.

Area of this room =Length x width

\(\begin{aligned}{c}A &= L \times W\\ = \left( {3.955 \pm 0.005{\rm{ }}m} \right) \times \left( {3.050 \pm 0.005{\rm{ }}m} \right)\\ &= 12.062{\rm{ }}{m^2}\end{aligned}\)

Hence, the area of this room is \(12.062{\rm{ }}{m^2}\).