Name________________________________ Circle practice
1. The equations 𝑥 2 + 𝑦 2 − 4𝑥 + 2𝑦 = 𝑏 describes a circle.
Part A:
Determine the 𝑦 − 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 of the center of the circle.
Part B:
The radius of the circle is 7 units. What is the value of 𝑏 in the equation?
From PARCC reference sheet:
2. A bike wheel has a diameter of 24 inches. How many revolutions will it make in order to have to
travel 2 miles? (In other words, how many circumferences of the circle are in 2 miles.)
3. Around the world in 80 days? If the diameter of the Earth is 12,800 kilometers, calculate your
speed in kilometers per hour if you were to take 80 days to circumnavigate the Earth distance
circumference about the equator.
𝑠𝑝𝑒𝑒𝑑 =
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑐𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒
=
𝑡𝑖𝑚𝑒
(80 𝑑𝑎𝑦𝑠 ∗ 24 ℎ𝑜𝑢𝑟𝑠)
1
4. An orbital mind control laser has been placed in a low orbit 200 miles above the Earth's surface.
Given that the radius of the Earth is approximately 4000 miles and that the satellite completes
an orbit in 12 hours, calculate the speed of the satellite in miles per hour.
5. You are keen to go on the merry-go-round with your friend. It is 30' in diameter and makes one
revolution every 10 seconds. You choose the "Prancing Bear" which is 8 feet from the center.
Your friend chooses the "Arabian stallion", which on the outer edge of the merry-go-round.
Once the merry-go-round starts your friend yells that they are going faster than you. You tell
them that's not true because you're both on the same merry-go-round. But as you think about
your Geometry you realize that she IS going faster. How much faster than you is your friend
going? Please give your answer in feet per second and also miles per hour.
2
6. A merry-go-round is set up at a local fair. The merry-go-round moves continuously at a rate
slow enough for riders to step on and off the ride. The pink horse, P, moves along the
circumference of the ride.
Hal used a coordinate grid to make a rough sketch of the merry-go-round, with the center at the
origin. Initially, P is at 𝑃(5,0). It takes 30 seconds for P to return to the same place.
What is the rate at the merry-go-around is turning, in feet per minute? Show your work.
Enter your answer and your work in the space provided.
Part B
What would be the coordinate of P on Hal’s sketch after 8.25 minutes?
Enter your answers in the boxes.
3
7. The circle has a radius of 12 units. Shade an area 24𝜋 square units. Divide the circle into the
correct number of sections. Then, select the number of sections represent the answer.
8.
9. A radio tower services a 10-mile radius. You stop your car 8 miles east and 8 miles north of the
tower. Will you be able to receive radio waves from the tower? (assume the center of the circle
is the origin).
4
10. Mr. Falcone's pizza shop offers three sizes of pizza. The small, medium and large pizzas have
diameters of 8 inches, 10 inches and 12 inches.
Small
Medium
Large
a) What is the circumference of each size of pizza?
Small = _________________ Medium = ___________________
Large = _______________
b) What is the area of each size of pizza?
Small = _________________ Medium = _________________
Large = _________________
c) Joey is very hungry. He says he wants to eat a 100-square-inch area of pizza. Which size(s) of
pizza should he order? Why?
11. The spray from a spinning lawn sprinkler covers an area of 625𝜋 square feet.
a) What is the radius of the circle covered by the lawn sprinkler?
Radius = ___________________________________________
b) If Andrew is standing 30 feet away from the sprinkler, will he get wet? Why or why not?
5