Question

The sum of the circumference and diameter of a circle is 116cm. Find its radius.

Answer 1

Hint: For the above question we will use the formula of the circumference of circle having diameter ‘d’ is equals to $'\pi d'$ where $\pi $ is a constant and equals to $\dfrac{22}{7}$. Also, we know that the radius of a circle is half of its diameter.

Complete step-by-step answer:
We have been given the sum of the circumference and diameter of a circle is 116cm.
Let the diameter of the circle be ‘d’ cm.
We know that circumference of a circle having diameter d is equal to $'\pi d'$ unit.
According to question, we have,
$\Rightarrow \pi d+d=116$
Taking ‘d’ as common, we get
$d\left( \pi +1 \right)=116$
Since, we know that $\pi =\dfrac{22}{7}$.
$\begin{align}
  & \Rightarrow d\left( \dfrac{22}{7}+1 \right)=116 \\
 & \Rightarrow d\left( \dfrac{22+7}{7} \right)=116 \\
 & \Rightarrow d\left( \dfrac{29}{7} \right)=116 \\
\end{align}$
On multiplying by 7, we get the equation as,
$\begin{align}
  & \Rightarrow 7\times \dfrac{d\times 29}{7}=116\times 7 \\
 & \Rightarrow d\times 29=116\times 7 \\
\end{align}$
On diving the equation by 29, we get,
$\begin{align}
  & \Rightarrow \dfrac{d\times 29}{29}=\dfrac{116\times 7}{29} \\
 & \Rightarrow d=\dfrac{116\times 7}{29}=28cm \\
\end{align}$
Hence, the diameter of the circle is 28cm.
Since, we know that the radius of a circle is half of the diameter of the circle.
$\Rightarrow radius=\dfrac{d}{2}=\dfrac{28}{2}=14cm$
Therefore, the radius is equal to 14cm.

Note: Don’t confuse between the formula of circumference of a circle in terms of diameter it is $\pi d$ and in terms of radius it is $2\pi r$. So, be careful while using it according to what you have been assumed or given.
Also, be careful sometimes we just equate circumference to $\pi d=116$ and we forget that we have been given that the sum of circumference and diameter is 116.