Question

At the park there is a pool shaped like a circle. A ring-shaped path goes around the pool. Its inner diameter is 22yd and its outer diameter is 32yd . 22yd 32yd. We are going to give a new layer of coating to the path. If one gallon of coating can cover 6yd2 , how many gallons of coating do we need?

Answer 1

First, we need to think about what we're actually solving for: the area of the path. To find this, we can find the area of the whole thing, minus the area of the pool.

The diagram would look something like the picture I attached. We know that to find the area of a circle, you do πr^2. The radius is half of the diameter, so halve the diameters:

22/2 = 11 yards
32/2 = 16 yards

Then solve for the area of both circles.
π$11^{2}$$= 121$π ≈ 380.13 (area of the pool)
π$16^{2}$$= 256$π ≈ 804.25 (area of the whole thing)

Next, subtract the area of the pool from the area of the whole thing to find the area of the walkway:
$804.25 - 380.13 = 424.12$ (area of the walkway)

Finally, divide the area of the walkway by 6 to see how many gallons of paint you'll need:

424.12 ÷ 6 ≈ 70.69

So you'll need 71 gallons of paint!

Hope I helped and let me know if you have any questions :)