Question

3 use different representations for π to calculate the area of a circle. a calculate the area of each circle with the given radius. round your answers to the nearest ten - thousandths, if necessary. value for π r = 6 units r = 1.5 units r = 1/2 unit use π key on a calculator use 3.14 for π use 22/7 for π π(6)^2 = 36π π(1.5)^2 = 2.25π π(1/2)^2 = 0.25π 113.1 sq. un 7.1 sq. cm 0.7 sq. in.

Explanation:

Step1: Recall area formula

The formula for the area of a circle is $A = \pi r^{2}$.

Step2: Calculate with $\pi = 3.14$ for $r = 6$ units

Substitute $r = 6$ and $\pi=3.14$ into the formula: $A=3.14\times6^{2}=3.14\times36 = 113.04$ square - units.

Step3: Calculate with $\pi=\frac{22}{7}$ for $r = 6$ units

Substitute $r = 6$ and $\pi=\frac{22}{7}$ into the formula: $A=\frac{22}{7}\times6^{2}=\frac{22}{7}\times36=\frac{792}{7}\approx113.1429$ square - units.

Step4: Calculate with calculator $\pi$ for $r = 6$ units

Using the calculator $\pi$ value, $A=\pi\times6^{2}=36\pi\approx36\times3.14159 = 113.09724\approx113.0972$ square - units.

Step5: Calculate with $\pi = 3.14$ for $r = 1.5$ units

Substitute $r = 1.5$ and $\pi = 3.14$ into the formula: $A=3.14\times1.5^{2}=3.14\times2.25 = 7.065$ square - units.

Step6: Calculate with $\pi=\frac{22}{7}$ for $r = 1.5$ units

Substitute $r = 1.5$ and $\pi=\frac{22}{7}$ into the formula: $A=\frac{22}{7}\times1.5^{2}=\frac{22}{7}\times2.25=\frac{49.5}{7}\approx7.0714$ square - units.

Step7: Calculate with calculator $\pi$ for $r = 1.5$ units

Using the calculator $\pi$ value, $A=\pi\times1.5^{2}=2.25\pi\approx2.25\times3.14159 = 7.06867\approx7.0687$ square - units.

Step8: Calculate with $\pi = 3.14$ for $r=\frac{1}{2}$ unit

Substitute $r=\frac{1}{2}$ and $\pi = 3.14$ into the formula: $A=3.14\times(\frac{1}{2})^{2}=3.14\times\frac{1}{4}=0.785$ square - units.

Step9: Calculate with $\pi=\frac{22}{7}$ for $r=\frac{1}{2}$ unit

Substitute $r=\frac{1}{2}$ and $\pi=\frac{22}{7}$ into the formula: $A=\frac{22}{7}\times(\frac{1}{2})^{2}=\frac{22}{7}\times\frac{1}{4}=\frac{22}{28}\approx0.7857$ square - units.

Step10: Calculate with calculator $\pi$ for $r=\frac{1}{2}$ unit

Using the calculator $\pi$ value, $A=\pi\times(\frac{1}{2})^{2}=\frac{\pi}{4}\approx\frac{3.14159}{4}=0.7854$ square - units.

Answer:

Value for $\pi$	$r = 6$ units	$r = 1.5$ units	$r=\frac{1}{2}$ unit
$\pi=\frac{22}{7}$	$\approx113.1429$ sq. units	$\approx7.0714$ sq. units	$\approx0.7857$ sq. units
Calculator $\pi$	$\approx113.0972$ sq. units	$\approx7.0687$ sq. units	$\approx0.7854$ sq. units