Question

At the park there is a pool shaped like a circle. A ring-shaped path goes around the pool. Its inner diameter is 14 yd and its outer diameter is 18yd.

We are going to give a new layer of coating to the path. If one gallon of coating can cover 4yd squared, 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 .)

Answer 1

26 gallons

Explanation:

We need to find the area of the ring-shaped path in order to determine how many gallons of coating we need.

First, we need to find the radius of the inner circle:

Radius = diameter/2 = 14 yd/2 = 7 yd

Next, we need to find the radius of the outer circle:

Radius = diameter/2 = 18 yd/2 = 9 yd

Now we can find the area of the ring-shaped path by subtracting the area of the inner circle from the area of the outer circle:

Area = π(9^2) - π(7^2) = π(81) - π(49) = 32π

Since we know that one gallon of coating covers 4yd squared, we can divide the area of the path by 4 to find how many gallons we need:

32π/4 = 8π

This is approximately 25.13, but since we can only buy whole gallons of coating, we need to round up to the nearest gallon.

Therefore, we need 26 gallons of coating to cover the path.

Answer 2

The area of the ring-shaped path can be found by subtracting the area of the inner circle from the area of the outer circle.

The area of the outer circle is:

A = πr^2 = 3.14(9^2) = 254.34 square yards

The area of the inner circle is:

A = πr^2 = 3.14(7^2) = 153.86 square yards

So, the area of the ring-shaped path is:

A = 254.34 - 153.86 = 100.48 square yards

Since each gallon of coating can cover 4 square yards, we need to divide the area of the path by 4 to find the number of gallons of coating needed:

100.48 / 4 = 25.12

We need 25 gallons of coating to cover the path.