A. How much greater is the area of a square with a side...

a. How much greater is the area of a square with a side length of 7 inches than the area of a circle with a radius of 4 inches? -1.24 square inches Preview b. How much greater is the area of a circle with a radius of 7.4 inches than the area of a square with a side length of 5.5 inches? 217.1416 square inches Preview c. Suppose the area of a circle with radius r is larger than the area of a square with side length l. Define a formula that expresses D, how much greater the area of a circle with radius r is than the area of a square with side length l, in terms of r and l. (That is, write a formula that expresses D in terms of r and l.) ? r^2 - l^2 Preview

Transcript

00:01 So in part a, we want to know how much greater is the area of a square that has a side length with 7 compared to the area of a circle that has a radius of 4 inches? well, remember, to find the area of a square, we just have to square the side length.

00:13 So in this case, because our side length is equal to 7, that means area would equal to 7 squared, which would be 49.

00:20 Now, our second shape is a circle, and to find the area of a circle, we have to do pi r square.

00:25 Well, in this case, we know that a radius is equal to 4.

00:28 So that means we would have pi times four squared.

00:31 4 squared is equal to 16.

00:33 So that would be 16 pi.

00:35 So if we're being asked to find how much greater is it, that would mean we have to take the area of the square, which is 49, and subtracted by the area of the circle, which is 16 pi.

00:45 So the difference would be 49 minus 16 pi.

00:48 So if you're allowed to have an exact answer, this would be it.

00:52 Or if you go to your calculator, you would do 49 minus 16 pi.

00:58 And it doesn't look like you're told what's around to.

01:01 So i'm just going to round two places after the decimal.

01:03 So what you would find is that it's approximately negative 1 .265.

01:11 Well, in this case, because they just want to know how much greater is that of the square, in this case, we know that the area of our circle is actually going to be larger.

01:21 So the difference in this case, like i said, is negative 1 .2.

01:25 And i apologize.

01:26 That should be negative 1 .27.

01:28 But that's how you would find the difference there.

01:30 Okay, part b.

01:32 It says, how much greater is the area of a circle with a radius of 7 .4? compared to the area of a square whose side length, i'm going to call that s, is equal to 5 .5.

01:45 So again, we have to find the area of both.

01:47 So we find the area of the circle.

01:49 Remember, we do pi times our radius, which is 7 .4 squared...

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