Question

A square tile of length 20 cm has four quarter circles at each corner (Fig. (1)). Find
or shaded portion. Another tile with same dimensions has a circle in the centre
(Fig. (11)). If the circle touches all the four sides of the square tile, find the area of the
portion. In which tile, area of shaded portion will be more? (lake it = 3.14)
). Find the area
in the which of the tile
area of the shaded
​

Answer 1

Answer:

(A) The Area of shaded portion is 86 cm²

(B) The Area of shaded portion is 86 cm²    

Step-by-step explanation:

Given as :

(A)

A square ABCD with side length = 20 cm

Four quarter circles are drawn at each corner

From The figure

Let The area of shaded portion = A sq cm

According to question

The area of square = side²

Or, The area of square = (20 cm) ²

or, The area of square = 400 cm²

Again

Area of circle = π r²           ,where r is radius of circle

So, Area of quarter circle = $\dfrac{1}{4}$ ×  π r²          

where r = 10 cm

So, The Area of 4 quarter circle each at four sides on square = 4 × $\dfrac{1}{4}$ ×  π r²          

Or, Area of 4 quarter circle =  π r² = 3.14 × (10 cm)²

i.e Area of 4 quarter circle = 314 cm²

Now,

Area of shaded region = Area of square - Area of 4 quarter circle

i.e A = 400 cm²  -  314 cm²

∴  A = 86 cm²

Hence,  The Area of shaded portion is 86 cm²  . Answer

(B)

From figure

A square ABCD with side length = 20 cm

∵ Area of square = side²

Or, Area of square = (20 cm) ²

Or, Area of square = 400 cm²

Again

The diameter of circle = side length of square

i.e D = 20 cm

So, radius = R = $\dfrac{D}{2}$   = $\dfrac{20}{2}$

i.e R = 10 cm

∵ Area of circle =  π R²

Or, Area of circle =  3.14 × (10 cm) ²

Or, Area of circle =  314 cm²

Now,

Area of shaded region = Area of square - Area of 4 quarter circle

A' = 400 cm² - 314 cm²

∴, A' = 86 cm²

Hence,  The Area of shaded portion is 86 cm²  . Answer

Answer 2

Answer

(A) The Area of shaded portion is 86 cm²

(B) The Area of shaded portion is 86 cm²

Step-by-step explanation:

Given as :

(A)

A square ABCD with side length = 20 cm

Four quarter circles are drawn at each corner

From The figure

Let The area of shaded portion = A sq cm

According to question

The area of square = side²

Or, The area of square = (20 cm) ²

or, The area of square = 400 cm²

Again

Area of circle = π r² ,where r is radius of circle

So, Area of quarter circle = \dfrac{1}{4}

4

1

× π r²

where r = 10 cm

So, The Area of 4 quarter circle each at four sides on square = 4 × \dfrac{1}{4}

4

1

× π r²

Or, Area of 4 quarter circle = π r² = 3.14 × (10 cm)²

i.e Area of 4 quarter circle = 314 cm²

Now,

Area of shaded region = Area of square - Area of 4 quarter circle

i.e A = 400 cm² - 314 cm²

∴ A = 86 cm²

Hence, The Area of shaded portion is 86 cm² . Answer

(B)

From figure

A square ABCD with side length = 20 cm

∵ Area of square = side²

Or, Area of square = (20 cm) ²

Or, Area of square = 400 cm²

Again

The diameter of circle = side length of square

i.e D = 20 cm

So, radius = R = \dfrac{D}{2}

2

D

= \dfrac{20}{2}

2

20

i.e R = 10 cm

∵ Area of circle = π R²

Or, Area of circle = 3.14 × (10 cm) ²

Or, Area of circle = 314 cm²

Now,

Area of shaded region = Area of square - Area of 4 quarter circle

A' = 400 cm² - 314 cm²

∴, A' = 86 cm²

Hence, The Area of shaded portion is 86 cm² . Answer

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