When you draw out the circle that is inscribed in a square, you should notice two things. The first thing you should notice is that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the side lengths of the square as its legs. The second thing you should notice is that the diameter of the circle has the same length as the length of one side of the square.

First, use the Pythagorean theorem to find the length of a side of the square.

$\displaystyle \text{Diagonal}^2=\text{side}^2+\text{side}^2$

$\displaystyle 2(\text{side})^2=\text{Diagonal}^2$

$\displaystyle \text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\displaystyle \text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Substitute in the length of the diagonal to find the length of the square.

$\displaystyle \text{side}=\frac{10(\sqrt2)}{2}$

Simplify.

$\displaystyle \text{side}=5\sqrt2$

Now, recall the relationship between the diameter of the circle and the side of the square.

$\displaystyle \text{diameter}=\text{side}=5\sqrt2$

When you draw out the circle that is inscribed in a square, you should notice two things. The first thing you should notice is that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the side lengths of the square as its legs. The second thing you should notice is that the diameter of the circle has the same length as the length of one side of the square.

First, use the Pythagorean theorem to find the length of a side of the square.

$\displaystyle \text{Diagonal}^2=\text{side}^2+\text{side}^2$

$\displaystyle 2(\text{side})^2=\text{Diagonal}^2$

$\displaystyle \text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\displaystyle \text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Substitute in the length of the diagonal to find the length of the square.

$\displaystyle \text{side}=\frac{20(\sqrt2)}{2}$

Simplify.

$\displaystyle \text{side}=10\sqrt2$

Now, recall the relationship between the diameter of the circle and the side of the square.

$\displaystyle \text{diameter}=\text{side}=10\sqrt2$

When you draw out the circle that is inscribed in a square, you should notice two things. The first thing you should notice is that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the side lengths of the square as its legs. The second thing you should notice is that the diameter of the circle has the same length as the length of one side of the square.

First, use the Pythagorean theorem to find the length of a side of the square.

$\displaystyle \text{Diagonal}^2=\text{side}^2+\text{side}^2$

$\displaystyle 2(\text{side})^2=\text{Diagonal}^2$

$\displaystyle \text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\displaystyle \text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Substitute in the length of the diagonal to find the length of the square.

$\displaystyle \text{side}=\frac{24(\sqrt2)}{2}$

Simplify.

$\displaystyle \text{side}=12\sqrt2$

Now, recall the relationship between the diameter of the circle and the side of the square.

$\displaystyle \text{diameter}=\text{side}=12\sqrt2$

When you draw out the circle that is inscribed in a square, you should notice two things. The first thing you should notice is that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the side lengths of the square as its legs. The second thing you should notice is that the diameter of the circle has the same length as the length of one side of the square.

First, use the Pythagorean theorem to find the length of a side of the square.

$\displaystyle \text{Diagonal}^2=\text{side}^2+\text{side}^2$

$\displaystyle 2(\text{side})^2=\text{Diagonal}^2$

$\displaystyle \text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\displaystyle \text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Substitute in the length of the diagonal to find the length of the square.

$\displaystyle \text{side}=\frac{26(\sqrt2)}{2}$

Simplify.

$\displaystyle \text{side}=13\sqrt2$

Now, recall the relationship between the diameter of the circle and the side of the square.

$\displaystyle \text{diameter}=\text{side}=13\sqrt2$

When you draw out the circle that is inscribed in a square, you should notice two things. The first thing you should notice is that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the side lengths of the square as its legs. The second thing you should notice is that the diameter of the circle has the same length as the length of one side of the square.

First, use the Pythagorean theorem to find the length of a side of the square.

$\displaystyle \text{Diagonal}^2=\text{side}^2+\text{side}^2$

$\displaystyle 2(\text{side})^2=\text{Diagonal}^2$

$\displaystyle \text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\displaystyle \text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Substitute in the length of the diagonal to find the length of the square.

$\displaystyle \text{side}=\frac{36(\sqrt2)}{2}$

Simplify.

$\displaystyle \text{side}=18\sqrt2$

Now, recall the relationship between the diameter of the circle and the side of the square.

$\displaystyle \text{diameter}=\text{side}=18\sqrt2$ 

When you draw out the circle that is inscribed in a square, you should notice two things. The first thing you should notice is that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the side lengths of the square as its legs. The second thing you should notice is that the diameter of the circle has the same length as the length of one side of the square.

First, use the Pythagorean theorem to find the length of a side of the square.

$\displaystyle \text{Diagonal}^2=\text{side}^2+\text{side}^2$

$\displaystyle 2(\text{side})^2=\text{Diagonal}^2$

$\displaystyle \text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\displaystyle \text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Substitute in the length of the diagonal to find the length of the square.

$\displaystyle \text{side}=\frac{48(\sqrt2)}{2}$

Simplify.

$\displaystyle \text{side}=24\sqrt2$

Now, recall the relationship between the diameter of the circle and the side of the square.

$\displaystyle \text{diameter}=\text{side}=24\sqrt2$

To solve, simply use the formula for area to solve for the radius and multiply by 2.

$\displaystyle A=\pi{r^2}\Rightarrow r=\sqrt{\frac{A}{\pi}}$

$\displaystyle r=\sqrt{\frac{16\pi}{\pi}}=\sqrt{16}=4$

$\displaystyle d=2r=2*4=8$

There are two steps to finding the answer to this question. The first is to find the radius through the formula for the circumference of a circle.

$\displaystyle Area = 2 (\pi) (r)$

Then we plug in numbers and solve. 

$\displaystyle 251.33 = 2 (\pi) (r)$

$\displaystyle 125.7 = \pi (r)$

$\displaystyle 40 = radius$

Now that we have found the radius, we solve for diameter by doubling it, since..

$\displaystyle Diameter = 2(Radius)$

Therefore, the diameter is equal to $\displaystyle 80 units$. 

To solve, simply use the formula for the diameter of a circle.

Recall that the diameter of a circle is twice the radius of the circle.

Given that the radius is seven, multiply it by 2 to solve for the diameter.

Thus,

$\displaystyle \\d=2r\\d=2*7\\d=14$.

To solve, simply use the formula for the area to find the length of the radius and then multiply that by 2 to find the diameter. Thus,

$\displaystyle A=\pi{r^2}\Rightarrow r=\sqrt{\frac{A}{\pi}}$

$\displaystyle r=\sqrt{\frac{9\pi}{\pi}}=\sqrt9=3$

$\displaystyle d=2r=2*3=6$