how many1.5 inch diameter pipes will be needed to have approximately the same total cross sectional area as one whose diameter is 5.0 inches?

Question

how do I figure this one out?

Answer 1

Use the formula for the area of a circle:

 

    A = πr² =π(d/2)² 

 

Area of 1.5 inch diameter pipe    =   π(1.5/2)²

Area of 5.0 inch diameter pipe    =   π(5.0/2)²

 

How many times as large (that is, how many small pipes to equal cross-sectional area of large pipe)?

       π(5.0/2)² / π(1.5/2)²

           5.0² / 1.5²

           25.00 / 2.25

           11.11

11 of the 1.5-inch diameter pipes are needed to have approximately the same total cross section as one 5.0-inch diameter pipe.