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}=(diameter)/(2) \\ \text{radius = }(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{ }(22)/(7) \\ \text{area}=(22)/(7)*6^2 \\ \text{area}=(22)/(7)*36 \\ \text{area}=(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=(22)/(7) \\ \text{circumference of the circle = 2}*(22)/(7)*6 \\ \text{circumference of the circle = }(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