Question

What is the diameter of a circle if its circumference is 25.8 inches?

Answer 1

Hint: Assume the diameter of the circle equal to d and radius of the circle as r. Now, use the formula: - \[d=2r\] to form a relation between the two terms. Use the formula: \[C=2\pi r\], where ‘C’ is the circumference of the circle, and equate the value of C = 25.8. Solve for the value of r to find the radius. Finally, use the relation between d and r to get the value of d as the answer. Substitute the value \[\pi =3.14\].

Complete step by step solution:
Here, we have been provided with the circumference of a circle and we are asked to determine its diameter.

Now, we know that the diameter (AB) of a circle is twice its radius (OB), so the relation between the two terms is given as:
\[\Rightarrow d=2r\] - (1)
Here d is the diameter and r is the radius of the circle.
Now let us find the circumference of the circle. Circumference of a circle is also called its perimeter and it is the length of the boundary of the circle. The circumference of the circle is given as: - \[C=2\pi r\], where ‘C’ denotes the circumference. According to the given question we have C = 25.8 inches, so substituting this in the formula we get,
\[\begin{align}
  & \Rightarrow 25.8=2\pi r \\
 & \Rightarrow r=\dfrac{25.8}{2\pi } \\
\end{align}\]
Multiplying both the sides with 2 and using relation (1) we get,
\[\begin{align}
  & \Rightarrow 2r=2\times \dfrac{25.8}{2\pi } \\
 & \Rightarrow d=\dfrac{25.8}{\pi } \\
\end{align}\]
Substituting the value \[\pi =3.14\] we get,
\[\begin{align}
  & \Rightarrow d=\dfrac{25.8}{3.14} \\
 & \therefore d\approx 8.22 \\
\end{align}\]
Hence the diameter of the circle is 8.22 inches.

Note: One may note that here we were not provided with the value of \[\pi \] in the question so we considered it equal to 3.14. You may take its value equal to \[\dfrac{22}{7}\]. It will not make much difference to our answer. You may also remember the direct relation between the circumference and diameter given as $C=\pi d$ to save the time.