Question

If the area of a circle is 201.06 cm squared, find its diameter and circumference.

Answer 1

`\large\boxed{\textsf{Diameter = 16 cm.}}`

`\large\boxed{\tt Circumference = 32\pi \ cm.}`

`\large\underline{\textsf{Or;}}`

`\large\boxed{\tt Circumference \approx 100.53cm.}`

Explanation:

`\textsf{We are asked for the Diameter, and the Circumference of a circle.}`

`\textsf{We are given the area. Let's review what information the area gives us.}`

`\large\underline{\textsf{Area Gives Us;}}`

`\textsf{Information that we have to find out.}`

`\textsf{We can receive the radius from the area by dividing the area by its own formula.}`

`\underline{\textsf{The Area of a Circle;}}`

`\tt Area = \pi r^(2)`

`\textsf{r represents the Radius.}`

`\large\underline{\textsf{Solving;}}`

`\textsf{Consider that we should divide by pi first, then square root both sides of the equation.}`

`\underline{\textsf{Divide by Pi;}}`

`\tt (201.06)/(\pi) = (\pi)/(\pi) r^(2)`

`\tt (201.06)/(\pi) \approx 64`

`\underline{\textsf{Square Root both sides of the equation;}}`

`\tt √(64) = \sqrt{r^(2)}`

`\tt r=8`

`\textsf{We know the Radius. Remember that the Diameter is twice the Radius.}`

`\large\boxed{\textsf{Diameter = 16 cm.}}`

`\textsf{Let's review what the Circumference is.}`

`\large\underline{\textsf{What is the Circumference?}}`

`\textsf{Circumference is the Perimeter of a Circle.}`

`\textsf{The curved edges of a circle make up the perimeter.}`

`\underline{\textsf{The Circumference of a Circle;}}`

`\tt Circumference = 2(Diameter * \pi)`

`\textsf{We know the Diameter, so we're able to solve.}`

`\large\underline{\textsf{Simplify;}}`

`\tt Circumference = 2(16 \pi)`

`\large\boxed{\tt Circumference = 32\pi \ cm.}`
`\textsf{(Exact)}`

`\large\underline{\textsf{Or;}}`

`\large\boxed{\tt Circumference \approx 100.53cm.}`
`\textsf{(Approximate)}`