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

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.

Answer 2

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

Explanation:

The area of a square is given by the formula

`area=width* 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.