Question

The diameter of a Frisbee is 12 in. What is the area of the Frisbee?

Answer 1

we know that

Area of the circle is equal to

$A=\pi r^{2}$

where

r is the radius

in this problem

$diameter=12\ in \\ radius=diameter/2\\ radius=12/2\\ radius=6\ in$

$A=3.14* 6^{2}$

$A=113.04 in^{2}$

therefore

the answer is the option

d. 113.04 sq. in.

Answer 2

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:

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

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!

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:

$A = \frac{1}{4} \pi d^2$

$A = \frac{1}{4} \times \pi \times 12^2$

$A = 36 \pi ~ in.^2$

$A \approx \boxed {113.10 ~ in.^2}$

The closest option available will be option D. 113 in.²

Learn more

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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 ,