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…

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asked Sep 22, 2023 136k views

1 Answer

Gourneau · Answer 1 · 2023-09-26T21:18:59+0000

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

$S=r^2\pi(A^o)/(360^o)$

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

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

$S=10^2\pi(110)/(360)=100\pi(11)/(36)\approx96.0$

And this is the area of the metal used.

Area = 96.0in²

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

$L=2\pi r(A^o)/(360^o)$

Again, just plugging our information:

$L=2\pi*10*(11)/(36)\approx19.2$

Length = 19.2in

And this is our answer.