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A bicycle is traveling at a constant rate such that the wheels rotate 72 degrees per 0.1 second. If each wheel of the bicycle has a diameter of 26 inches, how many inches does the bicycle travel in 2 seconds?
The circumference of a certain circular region is y.

Quantity A

The area of the circular region

Quantity B

$$\frac{y^{2}}{4}$$




The area of the shaded semicircular region is 64π.

Quantity A

The length of radius OR

Quantity B

10




In the figure above. O is the center of the circle. If minor arc AB has length 2π, what is the area of triangular region AOB?


The outline of a tyre can be roughly seen as two concentric circles. The radius of the larger circle is 8, while the radius of the smaller circle is 6. If the tyre revolve clockwise so that point y on the larger circle travels by d, then how long will a point x on the smaller circle travel?


The figure shows square ABCD inscribed in a circle. What is the ratio of arc ABC to the sum of lengths of line segments AB, BD and CD?


A pendulum 36 inches long swings through an angle of x degrees, and its pointed end travels through a distance of 41 inches before swinging back again, as shown in the figure. Which of the following is closest to the value of x?


In the above two concentric circles, the radius of the outside circle is twice as many as that of the inner one. Line segment BC is tangent to the inner circle. What is the central angle corresponding to arc ACB?


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


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, and the length of PN is $$2\sqrt{3}$$.

Quantity A

The circumference of the circle

Quantity B

36




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?
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?

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