Circles - scarsdaleschools.k12.ny.us



1) A bug crawls at a rate of 14π units per hour around a circle with a radius of 3.5 units. How many hours does it take the bug to complete 26 revolutions of the circle? (3) 2004-WU4-10

2) A bike’s front wheel has a 1-foot radius. How many revolutions does the wheel make in a one-mile trip? (2) 2004-WO2-7

3) A wheel has a circumference of 3 meters. The radius can be expressed as [pic] meters, with relatively prime integers A and B. What is the value of A + B? (3) 2004-WU6-4

4) A circular disk has a radius of two units. A point is marked on the edge of the disk. The disk rotates about its center, causing the point to travel a distance of 90 units. How many rotations did the disk make? Round to the nearest tenth. (2) 2004-WO3-10

5) A greeting card is six inches wide and eight inches tall. Point A is three inches from the fold, as shown. As the card is opened to an angle of 45º, how many inches does point A travel? Express your answer in terms of π. (2) 2004-WU8-7

A (

Happy

Birthday

6) A circular field circumscribes a plot of land that is 200 meters on each side, as shown. How many square meters of the circular region are not inside the square region? (3) 2004-WO4-7

200 m

7) The sum of the areas of the six congruent circles is 150π cm2. What is the area of the rectangle? (3) 2004-WU11-7

8) The students of Glenview Middle School are planning a carnival. One of the contests will be a dart throw. The radius of the entire round dartboard is eight inches. What is the radius of the shaded circle if the area of the non-shaded region is three times the area of the shaded region? (3) 2004-WU12-7

9) A carpenter wants to make the largest possible circular tabletop from a 4-foot by 8-foot sheet of plywood. If the tabletop is constructed from the two largest congruent semi-circular pieces that can be cut from the sheet, what is the diameter of the resulting table? (3) 2004-WU16-3

8 feet

10) The radius of circle O is 12, and [pic] and [pic] are tangent to the circle at B and D respectively. AB = 16, and CD = 5. What is the sum of OC and OA? (2) 1999-WU3-33

D C

O

A

B

11) Two small circles with radii 2 and 3 are externally tangent. A third circle is circumscribed about the first two as shown. What is the ratio of the area of the smallest circle to the area of the shaded region? (2) 1999-WU4-7

12) Two tangent congruent circles are circumscribed by a larger circle. The diameter of the larger circle is 24. Find the area of the shaded region. Express your answer in terms of π. (2) 1999-WU12-8

13) Square MNOP is tangent to circle O at N and P. What is the area of the shaded region? Round to the nearest whole number. (2) 2000-WU1-6

4 cm

14) In the circle, AP = 2 cm, PO = 3 cm, and m ................
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