Question

What is the diameter of a circle that has a circumference of $ 42'' $ ?

Answer 1

Hint: In order to determine the diameter of the circle with circumference of $ 42'' $ , first find the radius of the circle and then double the radius as diameter is equal to two times of the radius and hence our diameter is obtained.

Complete step by step solution:
We are given with the circumference of $ 42'' $ for a circle. In order to find the diameter of the circle we need to find the radius of the circle using the formula of circumference that is $ C = 2\pi r $ .
Since we have the value of circumference so just put the value of $ C $ in the above formula and we get:
\[
  C = 2\pi r \\
  42'' = 2 \times \dfrac{{22}}{7} \times r \\
  42'' = \dfrac{{44}}{7} \times r \\
  \dfrac{{42'' \times 7}}{{44}} = r \\
  r = 6.68'' \;
 \]
To find the diameter just double the radius obtained as we know that diameter is two times of the radius and we get:
 $
  d = 2r \\
  d = 2 \times 6.68'' \\
  d = 13.36'' \;
  $
Hence, the diameter of a circle that has a circumference of $ 42'' $ is $ 13.36'' $
So, the correct answer is “ $ 13.36'' $ ”.

Note: Circumference is the total distance once covered around the circle.
Diameter is the line that touches one side of the circle to another crossing through the centre of the problem.
Radius is half the diameter that is, it is the line from centre to the circle boundary.
 $ \pi $ is a mathematical constant and used in the calculations. Its value used is $ \dfrac{{22}}{7} $ .
We can directly get diameter just by dividing circumference by $ \pi $ that is: $ d = \dfrac{C}{\pi } $ then we would be left directly with $ 2r $ which is equal to the diameter of
the circle.