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masya89 [10]
3 years ago
6

If a sector in a circle of radius 10 has an area of 5pi, what is the measure of the central angle that forms the sector?

Mathematics
2 answers:
Degger [83]3 years ago
4 0

Answer:

pi/10

Step-by-step explanation:

Nadya [2.5K]3 years ago
3 0

Answer:

\frac{\pi }{10}

Step-by-step explanation:

The area (A) of the sector is calculated using the formula

A  = area of circle × fraction of circle

let x be the measure of the central angle, then

A = πr² × \frac{x}{2\pi } ← substitute values

5π = π × 10² × \frac{x}{2\pi }

5π = 100π × \frac{x}{2\pi } (cancel 50π and 2π )

5π = 50x ( divide both sides by 50 )

x = \frac{5\pi }{50} = \frac{\pi }{10} ← central angle

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