Question

Find the radius of the circle whose circumference is 176 cm.

Answer 1

Hint: To solve this question use the formula of circumference of the circle i.e. $circumference = 2\pi r$ ,where r is the radius of the circle.

Complete step-by-step answer:
We know that the circumference of a circle of radius r is given by $r = \dfrac{{circumference}}{{2\pi }}$
Putting circumference =176cm we get
\[176 = 2\pi r\]
Transposing LHS part to RHS and RHS to LHS we get
 \[\begin{gathered}
   \\
  2\pi r = 176 \\
\end{gathered} \]
Dividing both sides by $2\pi $ and solving we get
\[r = \dfrac{{176}}{{2\pi }}\] \[\]
Putting the value of $\pi = \dfrac{{22}}{7}$ in the expression we get
\[r = \dfrac{{176}}{{2 \times \dfrac{{22}}{7}}}\]
\[ \Rightarrow r = \dfrac{{176 \times 7}}{{2 \times 22}} \Rightarrow {\text{ }}r = 28{\text{cm}}\]

So, our answer i.e. required radius is 28cm.

Note: Circle is a closed 2D figure in which all points are at equal distance from a fixed point called center and this distance is called radius. If radius of circle is given and circumference is asked you can use $circumference = 2\pi r$,where r is radius of circle.