The area of the Frisbee is about 113 in.² ( Option D )
Further explanation
The basic formula that need to be recalled is:
Circular Area = π x R²
Circle Circumference = 2 x π x R
where:
R = radius of circle
The area of sector:
[tex]\text{Area of Sector} = \frac{\text{Central Angle}}{2 \pi} \times \text{Area of Circle}[/tex]
The length of arc:
[tex]\text{Length of Arc} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}[/tex]
Let us now tackle the problem!
Given:
Diameter of Frisbee = d = 12 in
Unknown:
Area of Frisbee = A = ?
Solution:
Area of the Frisbee could be calculated using the area of circle as follows:
[tex]A = \frac{1}{4} \pi d^2[/tex]
[tex]A = \frac{1}{4} \times \pi \times 12^2[/tex]
[tex]A = 36 \pi ~ in.^2[/tex]
[tex]A \approx \boxed {113.10 ~ in.^2}[/tex]
The closest option available will be option D. 113 in.²
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Answer details
Grade: College
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse, Circle , Arc , Sector , Area, Inches , Frisbee , Diameter , Radius , Trigonometry ,
