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Find the area of the shaded sector of the circle. Leave your answer in terms of pi.
(picture attached below)

Answer Choices:
A. (4 + 4(pi)) ft^2
B. (4 - pi) ft^2
C. (4 + pi) ft^2
D. (4 - 4(pi)) ft^2

thank you so much in advance! :)

Find the area of the shaded sector of the circle Leave your answer in terms of pi picture attached below Answer Choices A 4 4pi ft2 B 4 pi ft2 C 4 pi ft2 D 4 4p class=

Respuesta :

tiara143
The correct answer is option (B). The area of the shaded part is (4 - π) ft²


From the figure given below,

Area of the square = (side)²
                             
                              = (2 ft)²
                              
                              = 4 ft²

Area of the circle = π × (radius)²
                             
                              = π × (1 ft)²
                              
                              = π ft²

Area of the shaded part = Area of square - Area of circle 
                 
                                     = 4 ft² - π ft² 

                                    = (4-π) ft²
Ver imagen tiara143

Answer:

B. (4 - pi) ft²

Step-by-step explanation:

Given, the circle having diameter 2 ft is inscribed in a square having side 2 ft,

By the given figure,

The area of shaded region = Area of the square - Area of the circle

Now, the radius of the circle = diameter/2 = 2/2 = 1 ft,

Since, the area of circle = [tex]\pi[/tex] ( radius )²

Thus, the area of the given circle = [tex]\pi[/tex] (1)² = [tex]\pi[/tex] ft²,

Now, the area of a square = (side)²,

Here, the side of the given square = 2 ft,

⇒ The area of the given square = 2² = 4 ft².

Hence, the area of the shaded region = ( 4 - [tex]\pi[/tex] ) ft²

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