「Answer」AMC8 -- 2012年真题解析与视频讲解( 三 ) |area|that|be|

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Answer: B
Solution:
The value of 7/21 is 1/3. 5/19 is less than 5/15 (5/15=1/3). 9/23 is greater than 9/27(9/27=1/3). Thus 5/19 <7/21 <9/23.Problem 21

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Answer: D
Solution:
If Marla evenly distributes her 300 square feet of paint between the 6 faces, each face will get 300/6=50 square feet of paint. The surface area of one of the faces of the cube is 10*10=100 square feet. Therefore, there will be 100-50=50 square feet of white on each side.
Problem 22

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Answer: D
Solution:
First, we find that the minimum value of the median of will be .Then, we find that the maximum value of the median of R will be 9.
Problem 23

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Answer: C
Solution:
Area of equilateral triangle is s*s*sqrt(3) which s is the side length. A hexagon is composed of 6 little equilateral triangles. Let the side length of the triangle be 2s, the side length of the hexagon is s. The area of little equilateral (side length is s) of hexagon is 1/4 of the area of bigger equilateral triangle. (side length is 2s). Thus the area of hexagon is 6*1/4*4=6.
Problem 24

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Answer: A
Solution:
Draw a square around the star figure. The side length of this square is 4, because the side length is the diameter of the circle. The square forms 4-quarter circles around the star figure. This is the equivalent of one large circle with radius 2, meaning that the total area of the quarter circles is 4Pi. The area of the square is 16. Thus, the area of the star figure is16-4Pi. The area of the circle is 4Pi. Taking the ratio of the two areas, we find the answer is (4-Pi)/Pi.
Problem 25

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Answer: C
Solution:
The total area of the four congruent triangles formed by the squares is 5-4=1. Therefore, the area of one of these triangles is 1/4. The height of one of these triangles is a and the base is b. Using the formula for area of the triangle, we have ab/2=1/4. Multiply by 2 on both sides to find that the value of ab is 1/2.
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