Five squares of unit area are circumscribed by a circle as shown what is the radius of the circle

Using this square in a circle calculator, you can find the biggest square in a circle. It also helps you find the largest circle inside a square. Be it geometry 📐, construction 🏗️, or daily life 🚶, we often come across composite shapes such as a square circumscribing a circle 🔵 or a square inscribed in a circle. This calculator helps you find the dimensions 📏 of such shapes when one of the measurements is known!

Have you ever wondered 'What is the largest circular pizza 🍕 I can fit into this square 🔲 box?' or 'What is the largest square piece of cake 🎂 I can fit into this circular plate 🍽️?' or 'What is the largest circular indoor pool 🏊 I can fit into this square room?' Well, wonder no more! Because our square in a circle calculator will help you find the answers to these questions and more!

Using the square in a circle calculator, you can find any of the following:

Dimensions of the biggest square in a circle:
- To find this, enter the value of the circle's radius or area.
- The calculator will display the side length and area of the largest square that can fit inside the circle!
Dimensions of the largest circle inside a square:
- To find this, enter the value of the square's side or area.
- The calculator will display the radius and area of the largest circle that can fit inside the square!
Dimensions of a square with the same area as a circle:
- To find this, enter the value of the circle's radius or area.
- The calculator will display the side length of the square with the same area as the circle!
Dimensions of a circle with the same area as a square:
- To find this, enter the value of the square's side or area.
- The calculator will display the radius of the circle with the same area as the square!

You can thus use this square in a circle calculator in several different ways, depending on your need!

To know how to find the largest square in a circle using the square inside a circle calculator, do the following:

Key in the value of the circle's radius or area.
The calculator will find what size square fits in the circle using the formula:
side length = √2 × radius
The side length and the area of the square inside the circle will be displayed!

In this manner, you can find the maximal square that you can draw within a given circle.

To know how to find the largest circle in a square using the square inside a circle calculator, do the following:

Key in the value of the side or area of the square circumscribed about a circle.
The calculator will find what size circle fits in the square using the formula:

$length2\large\text{radius} = \frac{\text{side length}}{2}$
The radius and the area of the circle inside the square will be displayed!

In this manner, when a square is circumscribing a circle, you can find the radius and area of the circle.

Squaring a circle refers to finding a square with the same area as that of the circle.

For a circle with radius r, a square with the same area will have a side length of r√π. So, for example, if a given circle has a radius of 10 cm, then a square with the same area as the circle will have a side length of 10√π cm.

Alternatively, we can also convert a given square to a round shape by doing the reverse operation.

It's interesting to note that we can approximate a square to a circle by incrementally increasing the number of sides to get regular polygons such as pentagon, hexagon, heptagon, octagon, etc. until we end up with a circle ⭕.

Converting a square to a circle refers to finding a circle with the same area as the square. So if we want to convert a square to a round figure, the radius of the resulting circle will be s/√π, where s is the side of the square.

If we have a circle of radius 10 cm, then we can do the following to find the largest square inscribed in the circle:

The largest square inscribed in a circle of radius r will have a side length of r√2.
So for a circle of radius 10 cm, the largest square in it will have a side length of 10√2 cm.
This value of the side length can be approximated to 14.1421 cm.
The area of the square will be 200 cm².

If we have a square circumscribed about a circle with side 10 cm, then we can find the largest circle inscribed in the square as follows:

The largest circle inscribed in a square of side s will have a radius of s/2.
So for a square of side 10 cm, the largest circle in it will have a radius of 5 cm.
The area of the circle will be 78.54 cm².

If we have a square of side 10 cm, its area will be 100 cm². A circle with the same area will therefore have a radius of 10/√π, or 5.64 cm.

Given the radius(r) of circle then find the area of square which is Circumscribed by circle.Examples:

Input : r = 3 Output :Area of square = 18 Input :r = 6 Output :Area of square = 72

All four sides of a square are of equal length and all four angles are 90 degree. The circle is circumscribed on a given square shown by a shaded region in the below diagram.

Properties of Circumscribed circle are as follows:

The center of the circumcircle is the point where the two diagonals of a square meet.
Circumscribed circle of a square is made through the four vertices of a square.
The radius of a circumcircle of a square is equal to the radius of a square.

Formula used to calculate the area of circumscribed square is:
2 * r2 where, r is the radius of the circle in which a square is circumscribed by circle.
How does this formula work?
Assume diagonal of square is d and length of side is a.We know from the Pythagoras Theorem, the diagonal of a square is √(2) times the length of a side.
i.e d2 = a2 + a2

d = 2 * a2 d = √(2) * a Now, a = d / √2and We know diagonal of square that are Circumscribed by Circle is equal to Diameter of circle. so Area of square = a * a = d / √(2) * d / √(2)
= d2/ 2

= ( 2 * r )2/ 2 ( We know d = 2 * r )
= 2 * r2

cout << " Area of square = "

static int find_Area(int r)

public static void main(String[] args)

System.out.print(" Area of square = "

print(" Area of square = ", find_Area(r))

static int find_Area(int r)

public static void Main()

Console.WriteLine(" Area of square = "

echo ("Area of square = ");

document.write(" Area of square = "

Output:

Area of square = 18

Time Complexity: O(1)
Auxiliary Space: O(1)

Please suggest if someone has a better solution which is more efficient in terms of space and time.
This article is contributed by Aarti_Rathi. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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