A round metal duct has a cross-section area of 134 square inches. What is the duct's diameter? Use the rules for working with measurements.
A) The diameter is 10.3 in.
B) The diameter is 13.1 in.
C) The diameter is 26.1 in.
D) The diameter is 6.53 in.
E) The diameter is 52.2 in.

Question

Quizplus · Accepted Answer

We know that the cross-sectional area of the duct (A) is 134 square inches, and the formula for the area of a circle is A = πr^2 (where r is the radius). We want to find the diameter (d), which is 2r.

So we can rearrange the formula to solve for the radius:

A = πr^2

134 = πr^2

r^2 = 42.7

r ≈ 6.53

Then, to find the diameter:

d = 2r ≈ 13.1

Therefore, the diameter of the duct is 13.1 inches.

A Round Metal Duct Has a Cross-Section Area of 134