Kendall bought 3 glazed donuts and 3 filled donuts and they fit perfectly in the 9" by 6" box. what is the area of the bottom of the box (the shaded region) not covered by donuts?

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The area of the bottom of the box (the shaded region) not covered by donuts will be 13.94 in²

Explanation

1.   Across the length of the box, there are three filled donuts. That means the total diameter of three filled donuts = 9 inch

So, diameter of each filled donuts = inch and the radius inch.

Area of each filled donuts =   in²

So, the area covered by three filled donuts in²

2. Diameter of each glazed donuts = 3 in  and diameter of each small circle inside = 1 in

So, the radius of each glazed donuts in and radius of each small circle   in  

So, the area of each glazed donuts in²

The Area covered by three glazed donuts in²

3.  Total area covered by 6 donuts = 21.21 + 18.85 = 40.06 in²

Area of the box = (length) × (width) = (9 × 6)in² = 54 in²

So, the area of the bottom of the box (the shaded region) not covered by donuts = (54 - 40.06) in² = 13.94 in²

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8