### Home > INT2 > Chapter 8 > Lesson 8.4.2 > Problem8-96

8-96.

Use what you know about the area and circumference of circles to answer the questions below. Show all work. Leave answers in terms of $π$.

1. If the radius of a circle is $14$ units, what is its circumference? What is its area?

To calculate the area of a circle use $πr^2$, for the circumference use $2πr$.

area $= 196π$
circumference $= 28π$

2. If a circle has diameter $10$ units, what is its circumference? What is its area?

Use the formulas given in part (a). What is the radius of this circle?

3. If a circle has circumference $100π$ units, what is its area?

$100π = 2πr$  Solve for the radius then use the radius to calculate the area.

4. If a circle has circumference $C$, what is its area in terms of $C$?

$\frac{C}{2\pi}=r$

$\frac{C}{2\pi}=r$

$A=\pi{r^2}=\pi(\frac{C}{2\pi})^2$

$A=\frac{\pi C^2}{4\pi^2}=?$