Question

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! :)

Answer 1

B. (4 - pi) ft²

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 =
`\pi` ( radius )²

Thus, the area of the given circle =
`\pi` (1)² =
`\pi` 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 -
`\pi` ) ft²

Answer 2

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