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.

Explanation:

Step1: Recall circle - area and circumference formulas

The formula for the area of a circle is $A = \pi r^{2}$, and the formula for the circumference of a circle is $C=2\pi r$, where $r$ is the radius of the circle. Given $r = 8$ mm.

Step2: Calculate the exact area

Substitute $r = 8$ into the area formula: $A=\pi r^{2}=\pi\times(8)^{2}=64\pi$ mm$^{2}$.

Step3: Calculate the exact circumference

Substitute $r = 8$ into the circumference formula: $C = 2\pi r=2\pi\times8 = 16\pi$ mm.

Step4: Calculate the approximate area and circumference

For the approximate area, $A = 64\pi\approx64\times3.14159 = 201.06$ mm$^{2}$ (rounded to the nearest hundred - th).
For the approximate circumference, $C=16\pi\approx16\times3.14159 = 50.27$ mm (rounded to the nearest hundred - th).

Answer:

(a) Exact area: $64\pi$ mm$^{2}$, Exact circumference: $16\pi$ mm
(b) Approximate area: $201.06$ mm$^{2}$, Approximate circumference: $50.27$ mm