Four 8 inch pipes carry the same volume as which of the following?

To determine which option corresponds to the same volume as four 8-inch pipes, it’s essential to understand how the pipe diameter affects the flow capacity. The volume flow rate of a pipe is influenced by the area of the circular cross-section, 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 an 8-inch pipe, the area would be:

• Area = π(8/2)² = π(4)² = 16π square inches.

Thus, the flow area of one 8-inch pipe is 16π square inches. Therefore, four 8-inch pipes would have a total area of:

• Total area = 4 × 16π = 64π square inches.

Now, let's determine the equivalent diameter that would provide an area of 64π square inches. The area of a pipe can also be expressed in terms of its diameter:

64π = π(d/2)²

=> 64 = (d/2)²

=> d/2 = 8

=> d = 16 inches.

Hence, the total cross-sectional area of four 8-inch pipes is equivalent to