Question

Your bedroom has a rectangular shape and you want to measure its size. You use a tape that is precise to 0.001 m and find that the shortest wall in the room is 3.547 m 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 m. You measure the second wall to be 4.79 m 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) 30 m^2.
b) 31.4 m^2.
c) 31.37 m^2.
d) 31.371 m^2.

Answer 1

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?

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

Answer:

Part A

$A = 16.99 \ m^2$

Part  B

 $A_r =31.37 \ m^2$

Explanation:

From the question we are told that

   The  shortest wall is  $x = 3.547 \ m$

      The  length of the second wall is $y = 4.79 \ m$

Generally the area is mathematically evaluated as

           $A = x * y$

=>    $A = 3.547 * 4.79$

=>   $A = 16.99 \ m^2$

Given that the diameter is  d =  6.32

Then the area is  

         $A_r = \pi \frac{d^2}{4}$

         $A_r =3.142 * \frac{6.32^2}{4}$

        $A_r =31.37 \ m^2$