# The central angle of a sector is 72° and the sector has an area of #5pi#. How do you find the radius?

Area of a sector is:

So:

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To find the radius of the sector, use the formula for the area of a sector:

[ \text{Area of sector} = \frac{\text{Central angle}}{360^\circ} \times \pi r^2 ]

Given that the central angle is ( 72^\circ ) and the area of the sector is ( 5\pi ), plug these values into the formula and solve for the radius ( r ):

[ 5\pi = \frac{72}{360} \times \pi r^2 ]

[ 5\pi = \frac{1}{5} \pi r^2 ]

[ r^2 = \frac{5\pi}{\frac{\pi}{5}} ]

[ r^2 = 25 ]

[ r = \sqrt{25} ]

[ r = 5 ]

Therefore, the radius of the sector is ( 5 ) units.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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