Answer
397.5k+ views
Hint:First assume the perimeter of the square and circle and then equate the perimeters and then find the value of the sides \[s\] of the square and then equate the area of the square and circle. The formula for the square and circle as:
Area of square: \[{{s}^{2}}\]
Area of circle: \[\pi {{r}^{2}}\] (\[r\]: radius)
Complete step by step solution:
As given in the question, the circumference of the circle is equal to the value of the perimeter of the square, both square and circumference are the measurement of the outer boundary of the figure. Let us see the perimeter of the square which can be defined by the formula as:
\[\Rightarrow 4s\]
Whereas the perimeter of the circle is given as:
\[\Rightarrow 2\pi r\]
Now equating the perimeter of the square and circle together, we get the value of the sides of the square as:
\[\Rightarrow 4s=2\pi r\]
\[\Rightarrow s=\dfrac{2\pi r}{4}\]
\[\Rightarrow s=\dfrac{\pi r}{2}\]
Now as we have gotten the value of the sides of the square in terms of radius, we now equate the area of the square with the area of the circle and write the equation as:
Area of square \[=\] Area of circle
Placing the values in the above equation, we get the area of the circle to the area of the square as:
\[\Rightarrow {{\left( \dfrac{\pi r}{2} \right)}^{2}}=\pi {{r}^{2}}\]
\[\Rightarrow \dfrac{\pi {{r}^{2}}}{4}=\pi {{r}^{2}}\]
\[\Rightarrow \pi {{r}^{2}}\times \dfrac{4}{\pi {{r}^{2}}}\]
\[\Rightarrow \dfrac{4}{1}\]
Therefore, the ratio of the area of the circle and square as \[4:1\].
Note:
The circumference is same as the perimeter but for circular objects whereas both the perimeter and circumference is same as both of them are the measurement of the outer length of the object.
Area of square: \[{{s}^{2}}\]
Area of circle: \[\pi {{r}^{2}}\] (\[r\]: radius)
Complete step by step solution:
As given in the question, the circumference of the circle is equal to the value of the perimeter of the square, both square and circumference are the measurement of the outer boundary of the figure. Let us see the perimeter of the square which can be defined by the formula as:
\[\Rightarrow 4s\]
Whereas the perimeter of the circle is given as:
\[\Rightarrow 2\pi r\]
Now equating the perimeter of the square and circle together, we get the value of the sides of the square as:
\[\Rightarrow 4s=2\pi r\]
\[\Rightarrow s=\dfrac{2\pi r}{4}\]
\[\Rightarrow s=\dfrac{\pi r}{2}\]
Now as we have gotten the value of the sides of the square in terms of radius, we now equate the area of the square with the area of the circle and write the equation as:
Area of square \[=\] Area of circle
Placing the values in the above equation, we get the area of the circle to the area of the square as:
\[\Rightarrow {{\left( \dfrac{\pi r}{2} \right)}^{2}}=\pi {{r}^{2}}\]
\[\Rightarrow \dfrac{\pi {{r}^{2}}}{4}=\pi {{r}^{2}}\]
\[\Rightarrow \pi {{r}^{2}}\times \dfrac{4}{\pi {{r}^{2}}}\]
\[\Rightarrow \dfrac{4}{1}\]
Therefore, the ratio of the area of the circle and square as \[4:1\].
Note:
The circumference is same as the perimeter but for circular objects whereas both the perimeter and circumference is same as both of them are the measurement of the outer length of the object.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)