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QuestionFind the area of a circle centered at the origin with radius 15 using π≈3.14\pi \approx 3.14. Options: A. 47.1 B. 94.2 C. 225 D. 706.5 E. 2826

Studdy Solution

STEP 1

Assumptions1. The circle is centered at the origin (0,0). . The points (15,0), (0,15), (-15,0), and (0, -15) lie on the circle.
3. The value of π\pi is3.14.

STEP 2

The distance from the center of the circle to any point on the circle is the radius. We can use any of the given points to calculate the radius. Let's use the point (15,0).
Radius=(x2−x1)2+(y2−y1)2Radius = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}

STEP 3

Now, plug in the values for the center of the circle (0,0) and the point (15,0) to calculate the radius.
Radius=(15−0)2+(0−0)2Radius = \sqrt{(15 -0)^2 + (0 -0)^2}

STEP 4

Calculate the radius.
Radius=(15)2+(0)2=15Radius = \sqrt{(15)^2 + (0)^2} =15

STEP 5

Now that we have the radius, we can calculate the area of the circle using the formulaArea=πr2Area = \pi r^2

STEP 6

Plug in the values for π\pi and the radius to calculate the area.
Area=3.14times(15)2Area =3.14 \\times (15)^2

STEP 7

Calculate the area of the circle.
Area=3.14times225=706.5Area =3.14 \\times225 =706.5The area of the circle is706.5 square units. So, the correct answer is D.706.5.

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