Answer

Verified

354.1k+ views

Hint- The side of the square is given in question. Inscribed circle means the circle which lies inside this given square and circumscribed is the circle present in outer of this square. So, use the concept that the diagonal of the square is the diameter of the circle circumscribed and the side acts as the diameter of the circle inscribed in the square.

Now the side of a square AB=10cm.

So all sides are equal of a square hence AB=BC=CD=DA=10 cm

Thus all the sides will be equal to 10 cm only as the sides of the square are all equal.

So the diagonal of square is the diameter of the circumscribed circle thus

Diagonal AC will be using Pythagoras theorem in triangle ABC $hypotenou{s^2} = perpendicula{r^2} + bas{e^2}$

$ \Rightarrow A{C^2} = A{B^2} + B{C^2}$

Now AB=BC=10 cm (Sides of a square are equal)

$ \Rightarrow A{C^2} = {10^2} + {10^2} = 100 + 100 = 200$

Thus AC = $\sqrt {200} = 10\sqrt 2 {\text{ cm}}$……………………….. (1)

Now AC acts as diameter to the circumscribed circle hence

Diameter of circle circumscribed = $10\sqrt 2 {\text{ cm}}$

Thus $r = \dfrac{D}{2} = \dfrac{{10\sqrt 2 }}{2} = 5\sqrt 2 {\text{ cm}}$……………………. (2)

Now area of a given by Area = $\pi {r^2}$………………….. (3)

Putting equation (2) in equation (3)

Area = $\pi {(5\sqrt 2 )^2} = 3.14 \times 50 = 157{\text{ c}}{{\text{m}}^2}$

Now the side of the square will act as diameter to the circle inscribed to the square thus diameter of inscribed circle will be 10cm

Hence radius of inscribed circle = $\dfrac{{10}}{2} = 5{\text{ cm}}$……………………. (4)

Area of inscribed circle will be $\pi {(5)^2} = 3.14 \times 25 = 78.5{\text{ c}}{{\text{m}}^2}$ (Using equation 3 and 4)

Note- Whenever we face such problems the key concept we need to recall is the difference between the circumscribed and the inscribed circle of a square. By proper observation of the diagram it will be clear what will be the respective diameters of the circumscribed and the inscribed circle.

Now the side of a square AB=10cm.

So all sides are equal of a square hence AB=BC=CD=DA=10 cm

Thus all the sides will be equal to 10 cm only as the sides of the square are all equal.

So the diagonal of square is the diameter of the circumscribed circle thus

Diagonal AC will be using Pythagoras theorem in triangle ABC $hypotenou{s^2} = perpendicula{r^2} + bas{e^2}$

$ \Rightarrow A{C^2} = A{B^2} + B{C^2}$

Now AB=BC=10 cm (Sides of a square are equal)

$ \Rightarrow A{C^2} = {10^2} + {10^2} = 100 + 100 = 200$

Thus AC = $\sqrt {200} = 10\sqrt 2 {\text{ cm}}$……………………….. (1)

Now AC acts as diameter to the circumscribed circle hence

Diameter of circle circumscribed = $10\sqrt 2 {\text{ cm}}$

Thus $r = \dfrac{D}{2} = \dfrac{{10\sqrt 2 }}{2} = 5\sqrt 2 {\text{ cm}}$……………………. (2)

Now area of a given by Area = $\pi {r^2}$………………….. (3)

Putting equation (2) in equation (3)

Area = $\pi {(5\sqrt 2 )^2} = 3.14 \times 50 = 157{\text{ c}}{{\text{m}}^2}$

Now the side of the square will act as diameter to the circle inscribed to the square thus diameter of inscribed circle will be 10cm

Hence radius of inscribed circle = $\dfrac{{10}}{2} = 5{\text{ cm}}$……………………. (4)

Area of inscribed circle will be $\pi {(5)^2} = 3.14 \times 25 = 78.5{\text{ c}}{{\text{m}}^2}$ (Using equation 3 and 4)

Note- Whenever we face such problems the key concept we need to recall is the difference between the circumscribed and the inscribed circle of a square. By proper observation of the diagram it will be clear what will be the respective diameters of the circumscribed and the inscribed circle.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Guru Purnima speech in English in 100 words class 7 english CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Select the word that is correctly spelled a Twelveth class 10 english CBSE