Question

a circle has a radius of 14 feet .a. the exact area of the circle is ____ square feet. b. the approximate area of the circle is _____ square feet (use 22/7 as an approximation for pi . )c. the approximate circumference of the circle is _____ feet ( use 22/7 as an approximation for pi . )

Answer 1

We have that the radius of the circle is 14 feet, then the exact area is the following:

`\begin{gathered} A=\pi\cdot r^2 \\ \pi=3.1416 \\ r=14 \\ \Rightarrow A=(3.1416)(14)^2=615.7536 \\ A=615.7536ft^2 \end{gathered}`

next, if we use 22/7 instead of pi, we get the following:

`\begin{gathered} A_a=(22)/(7)(14)^2=616 \\ A_a=616 \end{gathered}`

finally, we know that the circumference of the circle can be calculated with the following equation:

`C=\pi\cdot d`

where d is the diameter of the circle. Since the radius is 14 feet, then the diameter will be the double of the radius, then d = 2*14=28, thus, the circumference of the circle is:

`\begin{gathered} C=((22)/(7))(28)=88 \\ C=88 \end{gathered}`