Question

At the park there is a pool shaped like a circle with diameter 20 yards . A ring-shaped path goes around the pool. Its width is 5 yards. We are going to give a new layer of coating to the path. If one gallon of coating can cover 5 yards, how many gallons of coating do we need? Note that coating comes only by the gallon, so the number of gallons must be a whole number. (Use the value 3.14 for pi.)

Answer 1

We have 2 concentric circles

Answer 2

To find the area of the outer ring, follow these steps

1) Find the area of the larger circle (call it A)
2) Find the area of the smaller circle (call it B)
3) Subtract the two areas: A - B

Answer 3

I found the area of the bigger circle which is 314 but how would i find the area of the smaller circle?

Answer 4

Would I do (2.5^2)(3.14)?

Answer 5

Keep in mind that the smaller circle has a diameter of 20 (so it has a radius of 10)

Answer 6

Area of smaller circle:

A = pi*r^2

A = pi*10^2

A = pi*100

A = 100pi

A = 100(3.14)

A = 314

So the area of the smaller circle is 314 square yards

Answer 7

And the area of the larger circle would be found with what equation?
(3.14)(2.5^2)?

Answer 8

(3.14)(15)^2

Answer 9

since the radius of the new larger circle is 15 yards

Answer 10

So the ending result would be 392.5?

Answer 11

good, now divide that by 5 (since 1 gallon of paint can do 5 square yards)

Answer 12

78.5?

Answer 13

so 79?

Answer 14

good, the answer is 79

Answer 15

Thank you so much!! :) :) That helped me a lot!

Answer 16

you're welcome

Answer 17

Do you know how to factor?

Answer 18

I do, what's your question?