Math, asked by ncraft65, 1 year ago

The diameter of the larger circle is 10.5 cm. The diameter of the smaller circle is 4.5 cm.

What is the best approximation for the area of the shaded region?

Use 3.14 to approximate pi.


70.7 cm²

86.5 cm²

102.4 cm²

282.6 cm²


The diameter of the larger circle is 10.5 cm. The diameter of the smaller circle is 4.5 cm.

What is the best approximation for the area of the shaded region?

Use 3.14 to approximate pi.


70.7 cm²

86.5 cm²

102.4 cm²

282.6 cm²






A semicircle and a quarter circle are attached to the sides of a rectangle as shown.

What is the area of this figure?

Use 3.14 for pi.

Enter your answer in the box. Round only your final answer to the nearest whole number.


cm²

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Answers

Answered by abhi569
22

Answer:

The best approximation for the area of the shaded region is 70.7 cm^2.

The area of the figure is 109 cm^2.


Step-by-step explanation:

===================================

Identities to be applied : -

1, Diameter of circle = 2 x radius

2. Area of circle = π x ( radius )^2

3. Area of rectangle = length x breadth

===================================


Solution :

Given,

    Diameter of larger cirlce = 10.5 cm

So,

⇒ Radius of larger of circle = 10.5 cm / 2

⇒ Radius of larger circle = 5.25 cm


From the properties given above,

⇒ Area of larger circle = π x ( 5.25 cm )^2

⇒ Area of larger circle = π x 5.25 x 5.25 cm^2

⇒ Area of larger circle =  27.5625 π cm^2


Also,

     Diameter of smaller circle = 4.5 cm

So,

⇒ Radius of smaller circle = 2.25 cm


From the properties given above,

⇒ Area of smaller circle = π x 2.25 x 2.25 cm^2

⇒ Area of smaller circle = 5.0625 x π cm^2

⇒ Area of smaller circle = 5.0625 π cm^2


On observing the diagram, we get :

⇒ Area of shaded portion = Area of larger circle - Area of smaller circle


From the above solution,

⇒ Area of shaded portion =  27.5625 π cm^2 - 5.0625 π cm^2

⇒ Area of shaded portion = π( 27.5625 - 5.0625 ) cm^2

⇒ Area of shaded portion = 3.14 x 22.5 cm^2

⇒ Area of shaded portion = 70.65 cm^2 ≈ 70.7 cm^2


Hence,

The best approximation for the area of the shaded region is 70.7 cm^2.



Question 2 : -

Solution : -

      On observing the diagram :

Radius of semi - circle & quarter circle = 6 cm

Length of rectangle = 12 cm

Breadth of rectangle = 2 cm


On the basis of the properties given above,

⇒ Total area = area of rectangle + area of semi circle + area of quarter circle

⇒ Total area = ( 12 x 2 ) + ( 1 / 2 x π( 6 )^2 ) + ( 1 / 4 x π( 6 )^2 ) cm^2

⇒ Total area = 24 + ( 1 / 2 x π ( 6 )^2 ){ 1 + 1 / 2 } cm^2

⇒ Total area = 24 + ( 1 / 2 x 3.14 x 36 )( 3 / 2 )  cm^2

⇒ Total area = 24 + 84.78 cm^2

⇒ Total area = 108.78 cm^2

⇒ Total area ≈ 109 cm^2


Hence,

The area of this figure is 109 cm^2.



ncraft65: thank you so much :D
abhi569: Welcome :-)
ncraft65: how did you figure that out though
abhi569: ??
Answered by peytskye
0

Answer:

The answer is 70.7.

Step-by-step explanation:

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