A model of the bean bag toss board that Scott made is shown. The eyes, nose, and mouth are holes cut in the board.
Which measurement is the best estimate of the area of the board that is left after the holes are cut for the eyes, nose, and mouth? Use 3 for pi. Use paper and pencil to find the answer.
Responses
A
9 5 ft2
89 5 ft 2 8
B
6 3 ft2
86 3 ft 2 8
C
7 3 ft2
87 3 ft 2 8
D
5 1 ft2
45 1 ft 2 4
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Since the holes for the eyes, nose, and mouth are circular, we can calculate their areas using the formula A = πr^2, where r is the radius of the hole.
Let's first find the area of the eyes:
The diameter of the eyes is 2 ft, so the radius is 1 ft.
The area of one eye is A = 3 * 1^2 = 3 ft^2.
Since there are two eyes, the total area of the eyes is 3 ft^2 * 2 = 6 ft^2.
Next, let's find the area of the nose:
The diameter of the nose is 1.5 ft, so the radius is 0.75 ft.
The area of the nose is A = 3 * 0.75^2 = 1.6875 ft^2.
Finally, let's find the area of the mouth:
The diameter of the mouth is 3 ft, so the radius is 1.5 ft.
The area of the mouth is A = 3 * 1.5^2 = 6.75 ft^2.
To find the total area left after cutting the holes, we subtract the sum of the areas of the holes from the total area of the board.
The total area of the board is not given, so we cannot determine the exact answer. Without further information, we cannot make an accurate estimate of the area left after cutting the holes. Therefore, none of the given options are the best estimate.