Question

The roller skating rink has a track that is arcular. The inside of the rink can't be used, but has a diameter of 12 feet. The track is 3 feet wide and goes around the outside of the rink. What is the approximate area of the track?

Answer 1

First, we need to compute the area of the inner circle

Area of a circle is computed as follows:

`A=(\pi\cdot D^2)/(4)`

Substituting with D = 12 ft:

`\begin{gathered} A=(\pi\cdot12^2)/(4) \\ A\approx113.1ft^2 \end{gathered}`

Next, we need to calculate the area of the outer circle (its diameter is 3 + 12 + 3 = 18 ft), as follows:

`\begin{gathered} A=(\pi\cdot18^2)/(4) \\ A\approx254.5ft^2 \end{gathered}`

Finally, the approximate area of the track is 254.5 ft² - 113.1 ft² = 141.4 ft²