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Semenov [28]
3 years ago
5

A circle with radius 5 has a sector with a central angle of 9/10 pi

Mathematics
2 answers:
Solnce55 [7]3 years ago
5 0

Answer:

35.33

Step-by-step explanation:

The circle with radius 5 has a sector with a central angle of 9/10 pi.

The area of a sector is given as:

A_s = \frac{\alpha }{2\pi} * \pi r^2

where α = central angle of the sector in radians

r = radius of the circle

The area of the sector is therefore:

A_s = \frac{\frac{9 \pi}{10} }{2 \pi} * (3.14 * 5^2)\\ \\A_s = \frac{9}{20} * 78.5\\\\A_s = 35.33

The area of the sector is 35.33.

andriy [413]3 years ago
3 0

Answer:

<h2>The area of the sector to nearest hundredth is 35.33</h2>

Step-by-step explanation:

Formula for calculating the area of a sector is given as \frac{\theta}{360} *\pi r^{2} where;

r is the radius of the circle

theta is the angle substended by the sector.

Given r = 5 and central angle theta = \frac{9 \pi}{10}

Area of the sector is expressed as shown;

= \frac{9\pi/10}{2\pi}*\pi (5)^{2}  \\= \frac{9\pi}{20\pi}*25\pi\\ = \frac{225\pi}{20} \\= 225*3.14/20\\= 35.33

The area of the sector to nearest hundredth is 35.33

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