Question

How do you find the diameter of a circle with circumference 4.5 inches?

Answer 1

Hint: We express the general expressions for a circle. We use the radius as r and the circumference as $ 2\pi r $ . We equate the value with the given value of 4.5 and find the value of r. then we multiply with 2 to get the value of the diameter.

Complete step by step answer:
Let us assume the radius of a circle is r units. This gives that the diameter of the circle is double the radius which is $ 2\times r=2r $ units.
We also know that the circumference of the circle with the radius r will be $ 2\pi r $ units.
Now, it is given that for a circle the circumference value is 4.5 inches.
This gives the equality of $ 2\pi r=4.5 $ . We have a linear equation of r. We solve it to find the value of r.
 $ \begin{align}
  & 2\pi r=4.5 \\
 & \Rightarrow r=\dfrac{4.5}{2\pi } \\
\end{align} $
We take the value of $ \pi $ as $ \dfrac{22}{7} $ and solve the equation.
The value of r is $ \Rightarrow r=\dfrac{4.5}{2\times \dfrac{22}{7}}=\dfrac{4.5\times 7}{2\times 22} $ .
Now multiplying the terms, we get $ r=0.716 $.

We need to find the diameter which is double the radius.
So, the diameter is $ 2r=2\times 0.716=1.4324 $ .
Therefore, the diameter of a circle with a circumference of 4.5 inches is 1.43 inches.

Note:
We have been asked to find the diameter. We can also express the circumference as the multiplication of diameter and the value $ \pi $ as $ 2\pi r=\pi \left( 2r \right) $ . We divide the value of circumference by $ \pi $ to get the diameter.