Problem Set

(Note: Figures are not drawn to scale.)

    1. Triangle ABC is inscribed in a circle, such that AC is a diameter of the circle (see figure). What is the circumference of the circle?

    2. A cylinder has a surface area of 360π and height of 3. What is the diameter of the cylinder’s circular base?

    3. Randy can run π meters every 2 seconds. If the circular track has a radius of 75 meters, how many minutes does it take Randy to run twice around the track?

    4. Randy then moves on to the Jumbo Track, which has a radius of 200 meters (as compared to the first track, with a radius of 75 meters). Ordinarily, Randy runs 8 laps on the normal track. How many laps on the Jumbo Track would Randy have to run in order to run the same distance?

    5. A circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide (see figure). What is the area of the walkway?

    6. A cylindrical water tank has a diameter of 14 meters and a height of 20 meters. A water truck can fill π cubic meters of the tank every minute. How long in hours and minutes will it take the water truck to fill the water tank from empty to half full?

    7. AC and DE are both diameters of the circle shown below. If the area of the circle is 180 units2, what is the total area of the shaded sectors?

    8. Jane has to paint a cylindrical column that is 14 feet high and that has a circular base with a radius of 3 feet. If one bucket of paint will cover 10π square feet, how many whole buckets does Jane need to buy in order to paint the column, including the top and bottom?

    9. A circular flower bed takes up half the area of a square lawn. If an edge of the lawn is 200 feet long, what is the radius of the flower bed? (Express the answer in terms of π.)

    10. If angle ABC is 40 degrees (see figure), and the area of the circle is 81π, how long is arc AXC?

    11. Triangle ABD is inscribed in a circle, such that AD is a diameter οf the circle and angle BAD is 45° (see figure). If the area οf triangle ABD is 72 square units, hοw much larger is the area οf the circle than the area οf triangle ABD?

    12. Triangle ABD is inscribed in a circle, such that AD is a diameter οf the circle. (Refer tο the same figure as fοr prοblem #11.) If the area οf triangle ABD is 84.5 square units, what is the length οf arc BCD?

    13. A is the center of the circle above.

      Quantity A Quantity B
      The perimeter of triangle ABC The perimeter of the shaded region

    14. In the figure shown, a circle with area π is inscribed in a square.

      Quantity A Quantity B
      The combined area of the shaded regions 1
    15. Quantity A Quantity B
      The combined area of four circles, each with radius 1 The area of a circle with radius 2