Question

Verify your previous answer by using the formula for The previuthe circumference of a circle.

Short answer

The previous answer is verified by using the formula for the circumference of a circle.

Step-by-step solution

Step 1. Given information

The previous answer is,

The length of the graph of$f\left(x\right)=\sqrt{9-x^2}$from$x=-3$to$x=3$is,$3\mathrm{\pi }$units.

Step 2.The arc length is half of the arc length of the circumference of a circle.

The given function is, $f\left(x\right)=\sqrt{9-x^2}$

Let $f\left(x\right)=y$.

$y=\sqrt{9-x^2}$

We know that $y=\sqrt{r^2-x^2}$

where $r$is the radius.

Now compare the above formula with the given equation.

We get, $r=3$.

So, the circumference of the circle is,$2\left(3\mathrm{\pi }\right)=6\mathrm{\pi }$units.

Step 3. The formula for the circumference of the circle is,

$C=2\mathrm{\pi r}$.

Substitute the known values in the formula.

role="math" localid="1648887635641" $C=2\mathrm{\pi }\left(3\right)$

$\mathrm{C}=6\mathrm{\pi }$units.

The circumference which is obtained from the previous answer is same as the the circumference which is obtained by the formula.

Therefore, the previous answer is verified by using the formula for the circumference of a circle.