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:

The question is incomplete.the complete question is giving below "College Physics 10+5 pts

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?

A. 17.0m^2

B. 16.990m^2

C.16.99m^2

D.16.9m^2

E. .16.8m^2

b. 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

Answers:

A. 17.0m²

B. 31.4m²

Explanation:

First, we determine the area of the room using the measured parameters I.e

Length=4.79 long

Breadth= 3.547 long

Hence area is calculated as

A=length *Breadth

A=4.79*3.547

A=16.99013m²

From the question the different measurements have different precision, the answer should match the number of significant figures of the least precisely known number in the calculation which is 3 significant digits.

Hence the correct answer will be 17.0m²

B. The are of a circle is express as

A=πd²/4

A=π(6.32)²/4

A=31.37069m²

The π and 4 are exact number they have no effect on the accuracy on the accuracy of the area. Hence we express the answer to the same significant figure as giving in the question..

The correct answer will be 31.4m²