Question

The circumference of the circle is \[{\text{176cm}}\], find it’s radius
A.\[{\text{68cm}}\]
B.\[{\text{18cm}}\]
C.\[{\text{28cm}}\]
D.\[{\text{2cm}}\]

Answer 1

Hint: As we know that the circumference of the circle is given by \[{{2\pi r}}\]. Equating the given value to the known formula
We can get the value of r .

Complete step-by-step answer:

We know that circumference of circle is \[{{2\pi r}}\], and given that Circumference of circle is 176cm
So, \[{{2\pi r = 176}}\]
\[ \Rightarrow {\text{r = }}\dfrac{{{\text{176}}}}{{{{2(\pi )}}}}\]
On substituting the value of \[{{\pi }}\] we get,
\[
   \Rightarrow {\text{r = }}\dfrac{{{\text{88}}}}{{{\text{(}}\dfrac{{{\text{22}}}}{{\text{7}}}{\text{)}}}} \\
   \Rightarrow {{r = 4 \times 7}} \\
   \Rightarrow {\text{r = 28cm}} \\
 \]
Hence we can see that option (c) is our required correct answer.

Note: Circle : A circle is a collection of points where all the points are equidistant from the given point called the centre “O”.
Circle Properties
Some of the important properties of the circle are as follows:
1.The circles are said to be congruent if they have equal radii.
2.The diameter of a circle is the longest chord of a circle.
3.Equal chords and equal circles have the equal circumference.
4.The radius drawn perpendicular to the chord bisects the chord.
5.A circle can circumscribe a rectangle, trapezium, triangle, square, kite.