Question

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

Answer 1

Hint: We’ve been given the value of the circumference of the circle, using the formula of the circumference of the circle which is $2\pi (radius)$, we’ll get an equation in radius.
Solving that equation we’ll get the value of the radius of the circle.

Complete step-by-step answer:
Given data: circumference of the circle=176cm
Let the radius of the circle be ‘r’

We know that the circumference$ = 2\pi (radius)$
Therefore, the circumference of the given circle$ = 2\pi r$
Substituting the value of circumference from the given data, we get,
$ \Rightarrow 176 = 2\pi r$
On Dividing both sides by 2, we get,
$ \Rightarrow 88 = \pi r$
On Dividing both sides by \[\pi \], we get,
\[ \Rightarrow \dfrac{{88}}{\pi } = r\]
On Substituting the value of \[\pi = \dfrac{{22}}{7}\] , we get,
\[ \Rightarrow \dfrac{{88}}{{\dfrac{{22}}{7}}} = r\]
On Multiplying the by the reciprocal of the denominator, we get,
\[ \Rightarrow r = 88\left( {\dfrac{7}{{22}}} \right)\]
On simplifying as $22 \times 4 = 88$, we get,
\[ \Rightarrow r = 4\left( 7 \right)\]
On simplifying the brackets, we get,
\[\therefore r = 28\]
Therefore, the radius of the circle is\[28cm\].

Note: Alternative method for the above solution can be
Let the diameter of the circle is d

We know that the circumference$ = \pi (diameter)$
Therefore, the circumference of the given circle$ = \pi d$
Substituting the value of circumference from the given data, we get,
$ \Rightarrow 176 = \pi d$
On Dividing both sides by \[\pi \], we get,
\[ \Rightarrow \dfrac{{176}}{\pi } = d\]
On Substituting the value of \[\pi = \dfrac{{22}}{7}\] , we get,
\[ \Rightarrow \dfrac{{176}}{{\dfrac{{22}}{7}}} = r\]
On Multiplying the by the reciprocal of the denominator, we get,
\[ \Rightarrow r = 176\left( {\dfrac{7}{{22}}} \right)\]
On simplifying as $22 \times 8 = 176$ , we get,
\[ \Rightarrow d = 8\left( 7 \right)\]
On simplifying the brackets, we get,
\[\therefore d = 56\]
Therefore, the diameter of the circle is \[56cm\]
We know that diameter of the circle is 2(radius of the circle)
i.e. \[d = 2r\]
On substituting the value of d, we get,
\[ \Rightarrow 56 = 2r\]
On dividing the equation by 2, we get,
\[ \Rightarrow r = 28\]
Therefore, the radius of circle is 28cm