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The radius of each of the three sectors shown above is 2. What is the total area of the three sectors?


In the figure, ARD is an arc of a circle centered at point O, ABCD is a rectangle, and CD=$$\frac{a}{2}$$ . What is the area of the shaded region?


The figure shows the design of a mosaic tile in which the four sides of the square are the diameters of four intersecting semicircles. Small blue stones are to be placed in the shaded regions and will cover 95 percent of the area of these regions. If each side of the square has length 2 feet, approximately how many square feet of the tile will be covered by the blue stones?


The circle, with a radius of 2, is equally divided by two perpendicular diameters as shown above. What is the area of the shaded area?
In the circle below, the center lies in point O, and AOB is a right-angled isosceles triangle.



Quantity A

The area of the triangular region AOB

Quantity B

Twice the area of the shaded area


As shown in the figure, the centers of the two circles are respectively on the circumference of each other, and the radius is 3. What is the perimeter of this figure?


The above two circles both have a radius of 5, and both pass through the center of the other circle.

Quantity A

The area of the shaded region

Quantity B

50π
The length of each side of a cubic box is 10.

Quantity A

The greatest possible number of identical spheres (whose diameter is 1) that can be put into the box

Quantity B

1000


The figure above shows a circle with center O. If the measure of angle ADC is 36 degrees and the length of arc ABC is 28, what is the circumference of the circle?


If O is the center of the circle, x=50, AC=BC, then what is the angle of ∠OBC?


In the figure above, BC is tangent to the circle with center O and radius 6. If BA=4, what is the area of the triangular region BCO?


In the figure, MN is tangent to the circle at point P, and O is the center of the circle. If the length of PN is $$2\sqrt{3}$$, what is the circumference of the circle?


In the figure above the circle has center O, and AB and AD are tangent to the circle. If the degree measures of angles ABC and ADC are 20 and 40, respectively, what is the value of x+y?


In the xy-plane shown, the circle is centered at the origin. Line $$l$$ passes through the origin and the point (3, 4). Line $$m$$ is tangent to the circle at the point (3, 4). What is the the x-intercept of line $$m$$?

Give your answer as a fraction.
A box manufacturer is designing a closed box in the shape of a rectangular solid. The ratio of the lengths of the sides of the box is 1 to 2 to 3. The total surface area of the box is 550 square inches. What is the volume of the box, in cubic inches?
There is a rectangular box with dimension 20 inches * 5 inches * 6 inches, the mass of the box is 17 kilograms, which of the following is closest to the density of the box in kilograms per cubic feet?

(note: density=mass/volume, 1 feet = 12 inches)
Two boxes R and S are of the same volume. They are both without top. R is a cube, while S has a base of a square. The height of the S is 8 times higher than the length. If the unit cost of each box is the same and the total cost for R is $6.00, what is the total cost for S?
A rectangular solid box has a height, width and length ratio of 1:2:3 and a volume of 750. What is the height of the box?
A certain type of storage container is in the shape of a rectangular solid that is 6 meters long, 2 meters wide, and 2.5 meters high. In a container ship, 12 of these storage containers were stacked together face to face to form a large rectangular block that is 12 meters long, 6 meters wide, and 5 meters high. The total surface area of all the container faces that are against other faces is approximately what percent of the surface area of the entire container stack?


X=The ratio of the area of the triangle ABC to the surface area of the entire cube

Quantity A

X

Quantity B

$$\frac{1}{6}$$

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