How much more water can a (17/32) sprinkler deliver than a (1/2) sprinkler?

To find how much more water a (17/32) inch sprinkler can deliver than a (1/2) inch sprinkler, it's essential to compare the two sizes based on their flow rates, which are related to their diameter. The flow rate is influenced by the diameter of the sprinkler head, where a larger diameter typically allows for more water to flow through it.

First, we convert the diameters into a common fraction. The (1/2) inch diameter equals (16/32) inches. Now, we can compare the two sizes:

1. The flow area of the (17/32) inch sprinkler can be calculated using the formula for the area of a circle, which is ( A = \pi (r^2) ) where r is the radius. The radius for (17/32) inches is (17/64) inches, and for (1/2) inch, the radius is (1/4) inches, or (16/64) inches.

2. By calculating the flow areas:

   • For (17/32) inch, the area would be ( A_1 = \pi \left(\frac{17/64}{2}\right)^2 = \pi \left(\