Question

What is the circumference of a circle with radius 16"?

Answer 1

Hint: We are given the radius of the circle and we need to find its circumference. For this we should be aware of the formula used for calculating the circumference of the circle which is $2\pi r$, where $r$ represents the radius of the circle. Here, we are given the radius in inches so the unit of the circumference would also be in inches. We can use either the decimal value of $\pi$ or the fractional approximation of $\pi$ to calculate the result.

Complete step by step solution:
We are given the radius of a circle. The term circumference means calculating the length of the boundary of the circle whose radius is given. We will use the following formula to calculate the circumference of the circle:
$\text{Circumference}=2\times \pi \times r$
Where $r$ is the radius of the circle. Here,
$r=16\text{ inches}$
We plug the value in the formula and we get:
$\text{Circumference}=2\times \pi \times 16\text{ inches}$
We can directly write the answer as $32\pi \text{ inches}$. But we can further give the whole answer in decimal or fraction by using the value of $\pi$. We put the value of $\pi$ to be equal to 3.14:
$\text{Circumference}=2\times \pi \times 16\text{ inches}$
$\text{Circumference}=100.48\text{ inches}$

Now, we can plug the value of $\pi$ to be ${\displaystyle \frac{22}{7}}$ and we get:
$\text{Circumference}=2\times {\displaystyle \frac{22}{7}}\times 16\text{ inches}$
$\text{Circumference}={\displaystyle \frac{704}{7}}\text{ inches}$
Hence, the circumference is calculated.

Note: The most frequent mistake that occurs while doing such questions is that you might end up using the formula for calculating the area of the circle instead of using the formula for calculating the circumference, so do take care of that.