Question

Find the perimeter and area of the circle which touches each side of a square of length 4cm

Answer 1

Step-by-step explanation:

We draw a radius at an angle of 90 degrees from the first radii.

We observe that a square is formed.

This shows us that half a side of square =4 cm

Thus, length of one side= 4×2=8 cm

Perimeter = 4×side=4×8=32 cm

Answer 2

Answer :-

• The perimeter and area of the circle which touches each side of a square of length 4 cm are 25.14 cm and 50.28 cm² respectively.

To find :-

• The perimeter and area of the circle which touches each side of a square of length 4 cm.

Step-by-step explanation :-

• Here, it is given that a circle touches each side of a square and length of each side of the square is 4 cm.  

 

As the circle touches each side of the square (Side of the square = 4 cm), the radius will be equal to the side of the square.

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• First let's find the perimeter (circumference) of the circle!  

We know that :-

$\underline{\boxed{\sf{Perimeter \: of \: a \: circle = 2 \pi r}}}$

Here,

• Radius = 4 cm.

• pi = 22/7.

Therefore,

$\longrightarrow \: \tt{Perimeter = 2 \times \dfrac{22}{7} \times 4}$

$\longrightarrow \: \tt{ Perimeter = \dfrac{44}{7} \times 4}$

$\longrightarrow \: \tt{Perimeter = \dfrac{176}{7}}$

$\longrightarrow \: \tt{Perimeter = 25.14\: cm}$

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• Now let's find the area of the circle!

We know that :-

$\underline{\boxed{\sf{Area \: of \: a \: circle = \pi {r}^{2}}}}$

Here,

• Radius = 4 cm.

• pi = 22/7.

Therefore,

$\longrightarrow \: \rm{Area =  \dfrac{22}{7} \times {4}^{2}}$

$\longrightarrow \: \rm{Area =  \dfrac{22}{7} \times 16}$

$\longrightarrow \: \rm{ Area = \dfrac{22}{7} \times 16}$

$\longrightarrow \: \rm{ Area = \dfrac{352}{7}}$

$\longrightarrow \: \rm{Area = 50.28\: cm^2}$

_____________________

Hence,

• The perimeter of the circle = 25.14 cm.
• The area of the circle = 50.28 cm².