Question

What will be the radius of the circle whose circumference will be $16\pi $ ?

Answer 1

Hint: Here, we are required to find the radius of the circle whose circumference is given to be $16\pi $ . First, we write down the formula of the circumference of a circle as $2\pi r$ and then equate it to the given value $16\pi $ . From here, after calculating we get the value of the radius as $8$ units.

Complete step by step solution:
Here, we are required to find the radius of the circle whose circumference is given to be $16\pi $ . The radius is denoted by “r” and the diameter is denoted by “d”. Circumference of a circle is the length of the curve that makes up the circle. We know that the radius of a circle is half of its diameter. This means that $r=\dfrac{d}{2}$ or that $d=2r$ .
The circumference of a circle is the product of the angle of a circle that is $2\pi $ and radius “r”. So, the circumference of a circle is equal to $2\pi r$ . The circumference is given as $16\pi $ . Since, the formula for circumference of a circle is $2\pi r$ , so we get,
$\begin{align}
  & 2\pi r=16\pi \\
 & \Rightarrow r=\dfrac{16}{2} \\
 & \Rightarrow r=8units \\
\end{align}$
Therefore, we can conclude that the radius of the circle with circumference $16\pi $ is $8units$.

Note: We can also solve the problem in another way. We rearrange the expression for circumference $16\pi $ as $2\pi \left( 8 \right)$ . Now, since the formula for the circumference of a circle is $2\pi r$ , so we can compare the two expressions and tell that the radius of the required circle is $8$ units.