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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

$$\frac{1}{6}$$
The larger of two right circular cylindrical containers has an inside radius of 3 inches, and the smaller has an inside radius of 1.5 inches; each of the containers has an inside height of 10 inches. If the smaller container were filled with water until the depth of the water was 9 inches, and then its water were poured into the empty larger container, what would be the depth of the water, in inches, in the larger container?
The volume of a cylinder is 54π and the height is 6. What is the circumference of the bottom of the cylinder?
A right circular cylinder with a volume of 16π is inscribed in a cube. What is the volume of the cube?


The figure shows a wooden toy wheel made by removing a smaller right circular cylinder from a larger right circular cylinder so that the cylinders are centered around the same axis. Line segments BC and AD are diameters of the smaller and larger cylinders, respectively, and line segment EF represents the width of both cylinders. The lengths, in centimeters, of BC, AD, and EF are 3, 7, and 2, respectively. Approximately what is the volume, in cubic centimeters, of the wood contained in the finished wheel?


The figure shows a right circular cone, where A is the center of the circular base. If the measure of angle ACB is 30°and the length of line segment BC is 2, what is the volume of the cone? (The volume of a right circular cone is one-third of the product of the height of the cone and the area of the circular base.)

Give your answer to the nearest whole number.


The volume V of the frustum of a right circular cone is given by V=($$\frac{πh}{3}$$)($$R^{2}$$+Rr+$$r^{2}$$), where h is the height of the frustum, R is the radius of its lower base, and r is the radius of its upper base, as shown. If the volume of the frustum of a right circular cone is 148π, its height is 12, and the radius of its upper base is 3, what is the radius of the lower base of the frustum?

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