Question

what is the area of the circle? what's the circumference? the diameter is 12 ft

Answer 1

Hello

to calculate the area and circumference of a circle, we need to know the formula for that

$\begin{gathered} \text{area of a circle }=\text{ }\Pi r^2 \\ circumference\text{ of a circle }=\text{ 2}\Pi r \end{gathered}$

r = radius of the circle

radius = diameter / 2

diameter = 12ft

$\begin{gathered} \text{radius}=\frac{diameter}{2} \\ \text{radius = }\frac{12}{2} \\ \text{radius }=\text{ 6ft} \end{gathered}$

substitute the value of radius in the formula to find the area and circumference of the circle

$\begin{gathered} area\text{ }=\text{ }\Pi r^2 \\ \Pi\text{ }=\text{ }\frac{22}{7} \\ \text{area}=\frac{22}{7}\times6^2 \\ \text{area}=\frac{22}{7}\times36 \\ \text{area}=\frac{792}{7} \\ \text{area}=113.14ft^2 \end{gathered}$

to find the circumference of the circle, let's substitute the values into the formula

$\begin{gathered} \text{circumference}=2\Pi r \\ \Pi=\frac{22}{7} \\ \text{circumference of the circle = 2}\times\frac{22}{7}\times6 \\ \text{circumference of the circle = }\frac{264}{7} \\ \text{circumference of the circle }=\text{ 37.71ft} \end{gathered}$

the area and circumference of the circle is 113.14ft^2 and 37.7ft respectively