Question

The circumference of the circle is 176 cm, find its radius.
A. 68 cm
B. 18 cm
C. 28 cm
D. 2 cm

Answer 1

Hint: We are given the value of circumference of the circle. We will substitute the values of circumference and $\pi = \dfrac{{22}}{7}$ in the formula of circumference of circle, $C = 2\pi r$, where $r$ is the radius of the circle. Solve the equation for the value of $r$.

Complete step-by-step answer:
We have been given that the circumference of a circle is 176 cm.
Radius is the distance from centre to the boundary of the circle.

We know that the circumference of a circle is given by $2\pi r$, where $r$ is the radius of the circle.
This implies, $2\pi r = 176$
On substituting the values of $\pi = \dfrac{{22}}{7}$, we will get,
$\Rightarrow$ $2\left( {\dfrac{{22}}{7}} \right)r = 176$
We will solve the above equation to find the value of $r$
$\Rightarrow$ $44r = 176 \times 7$
Divide both sides by 44
$\Rightarrow$ $r = 28$
Hence, the radius of the given circle is 28 cm
Thus, option C is correct.

Note: Circumference is the length of the boundary of the circle. We can also substitute $\pi = 3.14$ in the equation of circumference. The value of $2r$ is equal to the diameter of the circle, where $r$ is the radius of the circle.