Question

The table below lists the diameters of several circles. Find the area to the nearest whole number for each circle. Use as an approximation for .

Answer 1

The formula of the area of a circle is as follows:

`A=\pi r^2`

Since the diameter is twice the radius, we may rewrite the equation as follows:

`A=\pi\mleft(\cfrac{d}{2}\mright)^2`

where d is the diameter.

Thus, the area of Circle A is as follows:

`\begin{gathered} A_(CircleA)=\pi\mleft(\cfrac{12}{2}\mright)^2 \\ =\pi(6)^2 \\ =\pi(36) \\ \approx(3.14)(36) \\ \approx113.04 \\ \approx113 \end{gathered}`

The area of Circle B is as follows:

`\begin{gathered} A_(CircleB)=\pi\mleft(\cfrac{5}{2}\mright)^2 \\ =\pi(2.5)^2 \\ =\pi(6.25) \\ \approx(3.14)(6.25) \\ \approx19.625 \\ \approx20 \end{gathered}`

The area of Circle C is as follows:

`\begin{gathered} A_{\text{Circle C}}=\pi\mleft(\cfrac{24.8}{2}\mright)^2 \\ =\pi(12.4)^2 \\ =\pi(153.76) \\ \approx(3.14)(153.76) \\ \approx482.8064 \\ \approx483 \end{gathered}`