Answer
Verified
397.2k+ views
Hint: When a circle is inscribed in a square the diameter of the circle is equal to the side length of the square.
You can find the perimeter and area of the square, when at least one measure of the circle or the square is given.
For a square with side length S, the following formulas are used
Perimeter \[ = 4S\]
Area \[ = {S^2}\]
Diagonal \[ = S\sqrt 2 \]
For a circle write the radius r, the following formulas are used circumference \[ = 2\pi r\]
Area \[ = \pi {r^2}\]
Therefore,
Complete step-by-step answer:
As we know before the diameter of the circle is equal to the side length of the square.
The side length of the square \[ = 28\,cm\]
Area of a circle \[ = \pi {r^2}\]
To find the area first of all we find the radius of the circle.
\[d = 28\,cm\, = \]side length of the square
Where ‘d’ is diameter of the circle
\[r = \dfrac{d}{2} = \dfrac{{28}}{2} = 14\,cm\]
As we know that radius is half of the diameter
Now we have the value of ‘r’ that is 14 cm
Putting the value of r in the formula
Area of circle
\[ = \pi {r^2}\]
\[ = \pi \times {(14)^{2\,}}\,c{m^2}\]
\[ = 196\,\pi \,c{m^2}\]
Hence the area of the circle is \[196\,\pi \,c{m^2}\]
Note: If they ask to find the area of the square, we used the formula
Area of the square \[ = {S^2}\]
\[S = 28\,cm\]
\[ = 28 \times 28\,c{m^2}\]
\[ = 784\,c{m^2}\]
You can find the perimeter and area of the square, when at least one measure of the circle or the square is given.
For a square with side length S, the following formulas are used
Perimeter \[ = 4S\]
Area \[ = {S^2}\]
Diagonal \[ = S\sqrt 2 \]
For a circle write the radius r, the following formulas are used circumference \[ = 2\pi r\]
Area \[ = \pi {r^2}\]
Therefore,
Complete step-by-step answer:
As we know before the diameter of the circle is equal to the side length of the square.
The side length of the square \[ = 28\,cm\]
Area of a circle \[ = \pi {r^2}\]
To find the area first of all we find the radius of the circle.
\[d = 28\,cm\, = \]side length of the square
Where ‘d’ is diameter of the circle
\[r = \dfrac{d}{2} = \dfrac{{28}}{2} = 14\,cm\]
As we know that radius is half of the diameter
Now we have the value of ‘r’ that is 14 cm
Putting the value of r in the formula
Area of circle
\[ = \pi {r^2}\]
\[ = \pi \times {(14)^{2\,}}\,c{m^2}\]
\[ = 196\,\pi \,c{m^2}\]
Hence the area of the circle is \[196\,\pi \,c{m^2}\]
Note: If they ask to find the area of the square, we used the formula
Area of the square \[ = {S^2}\]
\[S = 28\,cm\]
\[ = 28 \times 28\,c{m^2}\]
\[ = 784\,c{m^2}\]
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE