Question

find the exact area of each circle.
1)

area =
2)

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3)

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4)

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1. if the radius is 10 ft, what will be the area of the circle?

a) ( 100 pi mathrm{ft}^{2} ) b) ( 400 pi mathrm{ft}^{2} ) c) ( 25 pi mathrm{ft}^{2} ) d) ( 2 pi mathrm{ft}^{2} )

1. what is the area of a circle with a diameter of 16 in?

a) ( 256 pi mathrm{in}^{2} ) b) ( 64 pi mathrm{in}^{2} ) c) ( 32 pi mathrm{in}^{2} ) d) ( 16 pi mathrm{in}^{2} )

1. a cow is tethered with a rope 20 ft long. what is the maximum area the cow can graze?

area =

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the circle.

Step2: Solve problem 7

Given \(r = 10\) ft. Substitute into the formula: \(A=\pi\times(10)^{2}=100\pi\) \(ft^{2}\).

Step3: Solve problem 8

Given \(d = 16\) in. First find \(r=\frac{d}{2}=\frac{16}{2}=8\) in. Then substitute into the formula: \(A=\pi\times(8)^{2}=64\pi\) \(in^{2}\).

Step4: Solve problem 9

The rope length is the radius \(r = 20\) ft. Substitute into the formula: \(A=\pi\times(20)^{2}=400\pi\) \(ft^{2}\).

Answer:

1. a. \(100\pi\ ft^{2}\)
2. b. \(64\pi\ in^{2}\)
3. \(400\pi\ ft^{2}\)