Question

Your bedroom has a rectangular shape, and you want to measure its area. You use a tape that is precise to 0.001 and find that the shortest wall in the room is 3.547 long. The tape, however, is too short to measure the length of the second wall, so you use a second tape, which is longer but only precise to 0.01 . You measure the second wall to be 4.79 long. Which of the following numbers is the most precise estimate that you can obtain from your measurements for the area of your bedroom?
If your bedroom has a circular shape, and its diameter measured 6.32 , which of the following numbers would be the most precise value for its area?

a) 30 m^2
b) 31.4 m^2
c) 31.37 m^2
d) 31.371 m^2

Answer 1

Answer:

(a) $17.0 m^{2}$

(b) $31.4 m^{2}$

Explanation:

(a)

The result obtained by multiplying two values which are having different precision has to express in the precision of the least precise number. So among the given values 4.79 is the least precise value; hence round off the result to 3 significant figures. For a rectangular room, area is a product of length and width, here, l is length and b is width/breadth

$Area=lb=4.79*3.547=16.9901\approx 17.0 m^{2}$

(b)

Following the same rules mentioned in part a of the question

For circular shaped bedroom, area $A={\pi (d/2)^{2}}$

$A=\pi\times (6.32/2)^{2}=31.37 m^{2}\approx 31.4 m^{2}$

The diameter of the circular room is 6.32, this is the least precise value used to calculate the area, so round off the final result to 3 significant figures