Area of plane figures: Find the angle of a sector whose arc length s 22cm and the area is 44cm

[yinkus]

Find the angle of a sector whose arc length s 22cm and the area is 44cm

 

[Dr.Peterson]

Find the angle of a sector whose arc length s 22cm and the area is 44cm

Please show whatever ideas you have about this, so we can see what help you need.

Also copy the problem correctly. An area can't be 44 cm!

 

[The Highlander]

Find the angle of a sector whose arc length s 22cm and the area is 44cm

Hello @yinkus,

Welcome to FMH.

I believe that @Dr.Peterson has suggested (above) that you haven't copied the problem out correctly because the area should be 44 cm² not just "44 cm".

However, I am concerned that failing to write the area as square cm (rather than just cm, as you did) may not be the only omission in your presentation of the problem!

Are you sure the problem did not also provide a length for the radius (r) of the circle that this sector is a part of? Were you not also given r as some even, whole number like 2, 4, 6, 8 or 10?

If you were given r then the problem becomes quite simple. All you need to know then is the formula for the Area of a sector (which you will need even if r wasn't given).

Alternatively, if r was not provided and the arc length and the area of the sector were, indeed, the only two values provided, then you will also need the formula for the length of an arc.

These formulae, the 'Area of a sector' and 'Arc length' may be found here and here, respectively (please study and memorize them).

Once you know them, you can transpose them to make r² and r the subject of the equations which will allow you to equate the expressions you now have, for r² & r (by squaring the latter) in order to find the measure of the angle (θ) subtended at the centre in this sector.

Please come back and show us the complete problem (in context and with any diagrams); a picture would be ideal.

Then also show us your attempt to solve the problem (a picture will also suffice for this) and it will be confirmed as correct or further advice will be offered if you are still having difficulty.

Hope that helps.

 

[Dr.Peterson]

Are you sure the problem did not also provide a length for the radius (r) of the circle that this sector is a part of? Were you not also given r as some even, whole number like 2, 4, 6, 8 or 10?

If you were given r then the problem becomes quite simple. All you need to know then is the formula for the Area of a sector (which you will need even if r wasn't given).

It isn't necessary to be given r; it turns out to be one of the numbers in your list, and if a different number were given, then the data would be inconsistent!

So, yes, both formulas are needed.

 

[The Highlander]

It isn't necessary to be given r; it turns out to be one of the numbers in your list, and if a different number were given, then the data would be inconsistent!

So, yes, both formulas are needed.

Yes, my suspicion was that the OP had been given r (making finding θ straightforward use of the Sector Area formula) and had simply failed to mention it in their presentation of the problem.

However, if, indeed, r wasn't given in the question, I didn't want to state what the value of r was explicitly; that is precisely why I included it in a list of numbers, to see if the OP would come back and say: "Oh, yes. I was given r as...". Clearly, I didn't want to just give the value of r (if it hadn't been included in the original question) as that would defeat the purpose of the exercise by simplifying the problem.

However, it looks like this is another one we'll never hear from again!
So maybe wait a few days and then someone can just post the solution for the sake of completeness.