Question

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?

Answer 1

Answer:

The area of the square is 1.266 $in^2$ less than the circle.

Step-by-step explanation:

The area of a square is given by the formula

$area=width\times height$

But since the width and height are by definition the same, the formula is usually written as

$area=s^2$

where s is the length of one side.

Given the radius of a circle, the area inside it can be calculated using the form

$area=\pi r^2$

where r is the radius of the circle and $\pi$  is Pi, approximately 3.142.

So, the area of a square with a side length of 7 inches is

$area_{square}=7^2=49\:in^2$

the area of a circle with a radius of 4 inches is

$area_{circle}=\pi 4^2=3.142\cdot 16=50.266 \:in^2$

Now, we take the difference in the areas.

$area_{square}-area_{circle}=49-50.266=-1.266\:in^2$

Because the difference between the areas of the square and the circle is negative, the area of the square is 1.266 $in^2$ less than the circle.

Answer 2

To find the area of the square, all you have to do is 7^2 which is 49.
The area of a circle is pi x 4^2
16pi = 16 x 3.14 = 50.24
The square is 1.24 inches squared less than that circle.