Question

5.Sheet Metal Trades A transition duct is constructed from a circular sector of radius 10 in. andangle 110 degrees. (a) What is the area of the metal used? (b) Calculate the arc length of thesector. (Round to the nearest tenth.)

Answer 1

The area of a circle sector is given by the following equation:

$S=r^2\pi\frac{A^o}{360^o}$

Where 'r' represents the radius and 'A' represents the angle.

Then, just plugging our information in this equation we get the following:

$S=10^2\pi\frac{110}{360}=100\pi\frac{11}{36}\approx96.0$

And this is the area of the metal used.

Area = 96.0in²

Now, for the arc length, we have the following formula:

$L=2\pi r\frac{A^o}{360^o}$

Again, just plugging our information:

$L=2\pi\times10\times\frac{11}{36}\approx19.2$

Length = 19.2in

And this is our answer.