Question

the radius of a circle is 8 mm. answer the parts below. make sure that you use the correct units in your answers. if necessary, refer to the list of geometry formulas. (a) find the exact area and circumference of the circle. write your answers in terms of π. exact area: exact circumference: (b) approximate the area and circumference of the circle. to do the approximations, use the π button on the aleks calculator and round your answers to the nearest hundredth. approximate area: approximate circumference:

Explanation:

Step1: Recall circle - area formula

The formula for the area of a circle is $A = \pi r^{2}$, where $r$ is the radius. Given $r = 8$ mm.
$A=\pi\times(8)^{2}=64\pi$ mm$^{2}$

Step2: Recall circle - circumference formula

The formula for the circumference of a circle is $C = 2\pi r$. Given $r = 8$ mm.
$C = 2\pi\times8=16\pi$ mm

Step3: Approximate the area

Using $\pi\approx3.14$, $A = 64\pi\approx64\times3.14 = 200.96$ mm$^{2}$

Step4: Approximate the circumference

Using $\pi\approx3.14$, $C=16\pi\approx16\times3.14 = 50.24$ mm

Answer:

(a) Exact area: $64\pi$ mm$^{2}$
Exact circumference: $16\pi$ mm
(b) Approximate area: $200.96$ mm$^{2}$
Approximate circumference: $50.24$ mm