Math $1145---$ Written Assignment $2$

You have design that originally calls for a rectangular duct that has a $8^{\text{'}\text{'}}{16}^{\text{'}\text{'}}$ end and is $160$ inches long. You need to replace this duct with a circular duct that has the same cross$-$sectional area.

SHOW YOUR WORK FOR THE FOLLOWING QUESTIONS: $(8$ marks$)$

a$)$ What diameter circular duct should selected?

b$)$ How many square feet of material would be needed to make the circular duct you selected if the duct is $160$ inches long $($assume the duct seams are welded so seam allowance is not a concern$)$

c$)$ How many square feet of material would be needed to make the originallyspecified rectangular duct if the duct is $160$ inches long? $($assume the duct seams are welded so seam allowance is not a concern$)$

d$)$ A design change indicates that the circular duct in part $($a$)$ needs to be replaced with a duct that has $2\mathrm{.}7$ times the cross$-$sectional area. What diameter duct should be selected?