Question

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

Answer 1

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

Further explanation

The basic formula that need to be recalled is:

Circular Area = π × R²

Circle Circumference = 2 × π × R

where:

R = radius of circle

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.

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

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

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

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

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

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Answer details

Grade: College

Subject: Mathematics

Chapter: Trigonometry

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

Answer 2

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.