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garik1379 [7]
3 years ago
14

Please please help!! I'm not sure if I have the right answer!!

Mathematics
2 answers:
3241004551 [841]3 years ago
7 0

The area of the sector formed by central angle AOB is 5/8 of the area of the circle

<h3>Further explanation</h3>

The basic formula that need to be recalled is:

Circular Area = π × R²

Circle Circumference = 2 × π × R

where:

<em>R = radius of circle</em>

The area of sector:

\text{Area of Sector} = \frac{\text{Central Angle}}{2 \pi} \times \text{Area of Circle}

The length of arc:

\text{Length of Arc} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}

Let us now tackle the problem!

This problem is about finding the area of the sector.

We can find a comparison of the area of the sector with the area of a circle with the following formula.

\text{Area of Sector} = \frac{\text{Central Angle}}{2 \pi} \times \text{Area of Circle}

\frac{\text{Area of Sector}}{\text{Area of Circle}} = \frac{\text{Central Angle}}{2 \pi}

\frac{\text{Area of Sector}}{\text{Area of Circle}} = \frac{5 \pi / 4}{2 \pi}

\frac{\text{Area of Sector}}{\text{Area of Circle}} = \frac{5 / 4}{2}

\frac{\text{Area of Sector}}{\text{Area of Circle}} = \large {\boxed {\frac{5}{8}} }

<h3>Learn more</h3>
  • Calculate Angle in Triangle : brainly.com/question/12438587
  • Periodic Functions and Trigonometry : brainly.com/question/9718382
  • Trigonometry Formula : brainly.com/question/12668178

<h3>Answer details</h3>

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse, Circle , Arc , Sector , Area

lana [24]3 years ago
6 0

Answer: The area of the sector formed by central angle AOB is 5/8 th of the total area of the circle.

Step-by-step explanation:

Let r be the radius of the circle having the center O,

⇒ The area of the circle = \pi r^2  square unit.

And, the central angle AOB = \frac{5\pi}{4}\text{ radian}

=(\frac{5\pi}{4}\times \frac{180}{\pi})^{\circ}  ( since, \pi = 180° )

=(\frac{900}{4})^{\circ}

=225^{\circ}

Hence, the area of sector AOB

=\frac{225^{\circ}}{360^{\circ}}\times \pi r^2

=\frac{5}{8}\times \pi r^2 square unit.

Now,

\frac{\text{Area of sector AOB}}{\text{Area of circle}}=\frac{\frac{5}{8}\times \pi r^2}{\pi r^2}

=\frac{5}{8}

⇒ Area of sector AOB = 5/8 × Area of the circle.

Hence, the area of the sector formed by central angle AOB is 5/8 th of the total area of the circle.

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