Question

A square room has a floor area of 81 meters. The height of the room is 5 meters?

Answer 1

To calculate the area of a square room, we square the length of one side. In this case, the length of one side is the square root of the floor area. So, if the floor area is 81 square meters, the length of one side is 9 meters. The volume can be found by multiplying the area of the base by the height.

Step-by-step explanation:

To calculate the area of a square room, we square the length of one side. In this case, the length of one side is the square root of the floor area. So, if the floor area is 81 square meters, the length of one side is sqrt(81) = 9 meters. Since a square has equal sides, the width of the room is also 9 meters. Therefore, the dimensions of the room are 9 meters by 9 meters.

To calculate the volume of the room, we multiply the area of the base by the height. The area of the base is 9 meters * 9 meters = 81 square meters. The height of the room is given as 5 meters. So, the volume of the room is 81 square meters * 5 meters = 405 cubic meters.

Answer 2

To calculate the area of the rectangular room, the length and width are multiplied, resulting in an area of approx. 12.07775 m². The relative uncertainties of the length and width are added together and then multiplied by the area to find the uncertainty, which is approximately 0.4 m².

Step-by-step explanation:

The question refers to the calculation of the area of a room given the measurements of its length and width, including the consideration of measurement uncertainty. To calculate the area of a rectangular room with given measurements, we use the formula Area = Length × Width.

Given the measurements are 3.955 ± 0.005 m for the length and 3.050 ± 0.005 m for the width, we can calculate the area by multiplying these two values together. To find the uncertainty of the area, we add the relative uncertainties of the length and width measurements and multiply the sum by the calculated area.

The calculated area is 12.07775 m² (3.955 m × 3.050 m). Each measurement has a relative uncertainty of 0.005/Measure, so for the length (0.005/3.955) and width (0.005/3.050), when added together, we get the total relative uncertainty. This total relative uncertainty is then multiplied by the calculated area to find the uncertainty in square meters, which in this case would be approximately 0.4 m², considering significant figures and rounding.