Length of arc and area of a sector (3 Viewers)

BlueGas · Apr 21, 2015

InteGrand said:
Yes, the method is right, but you'll get some error if you round before the final calculation (and the answer in this case is a whole number).

Plus, when you found the radius, you had to divide by $2\pi$ , and then multiply by a $2\pi$ again right after, so it's much more efficient in this case just to use $\frac{1}{3}$ straightaway.

Is there a formula that could be used for any question that contains circumference, degrees, radians, etc?

InteGrand · Apr 21, 2015

BlueGas said:
Is there a formula that could be used for any question that contains circumference, degrees, radians, etc?

Pretty much, if the Q is just asking for arc length.

Here are some general formulae. I'm going to use R for radius of the circle and C for the circumference of the full circle. The equation connecting these two is $C=2\pi R$ .

$\text{arc length} = R\times \text{central angle in radians}= \frac{C}{2\pi}\times \text{central angle in radians}=\frac{\text{central angle in degrees}}{360 ^\circ}\times C = \frac{\text{central angle in degrees}}{360 ^\circ}\times 2\pi R$ .

So you can use the one that is suitable for the data they've given you. But there's no need to memorise these, they're easily derivable from each other, you just need to know one of them and the fact that $C=2\pi R$ .

Length of arc and area of a sector (3 Viewers)

BlueGas

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InteGrand

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