How much more water can a 6-inch diameter pipe carry compared to a 3-inch diameter pipe?

To understand the carrying capacity of pipes of different diameters, one should consider the relationship between the diameter of the pipe and its cross-sectional area. The flow of water through a pipe is primarily determined by this area, which can be calculated using the formula for the area of a circle: A = π(d/2)², where d is the diameter of the pipe.

For a 3-inch diameter pipe, the area would be:

A₁ = π(3/2)² = π(2.25) ≈ 7.07 square inches.

For a 6-inch diameter pipe, the area would be:

A₂ = π(6/2)² = π(9) ≈ 28.27 square inches.

Now, to find out how much more water the 6-inch pipe can carry compared to the 3-inch pipe, we can take the ratio of the areas:

Ratio = A₂ / A₁ = 28.27 / 7.07 ≈ 4.

This means that a 6-inch diameter pipe can carry approximately four times as much water as a 3-inch diameter pipe, which is why the correct answer is four times as much. Understanding this relationship is crucial