Name________________________________
From PARCC reference sheet:
Write answers both as exact values and with decimal approximations to the nearest tenth.
1. 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.)
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2. 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)
3. 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.
4. Jenna drove her new Monster Truck to school. To show everyone just how monstrous it is, she
rolled the spare tire out into the parking lot. It took five students all holding hands to reach
around the tire. The heights of these kids are 62", 70",62",60" and 61 ". Did you know that a
person's height and arm span are approximately the same? Use this information to determine
an approximate tire radius.
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5. My son Scotty is holding onto the aglet (the little plastic thing on the end of the shoelace. Yes,
it's really called that.) of his shoelace and is swinging his shoe around his head. The swinging
shoe circle around his head has a radius of 18 inches. If the shoe makes the trip around his head
in 1 second, what is the speed of the shoe? (Express your answer in inches per second and in
feet per second)
6. Zachary's Pizza on 6th sells its Flying Z pizza (spinach, garlic, pineapple and jalepenos) in three
sizes for three prices: 12" diameter pie for $12.75, 14" pie for $14.25 and an 18" pie for $20.50.
Because the edge is the thickest (and therefore the best) part of the pie, calculate which size
gives the most pizza edge per dollar. (To do this you will need to find the circumference of each
pizza.)
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7. 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.
8. 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?
9. The earth has a diameter of 7926.41 miles. What is the circumference of the earth? (This
would be the distance you would have to walk, if you could walk around the equator.)
Circumference = _________________________________
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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. A bicycle wheel has a diameter of 21 inches. What is the circumference of this wheel? What is
the radius?
Radius = ______________________________
Circumference = ________________________________
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12. A Ferris wheel has a radius of 65 feet. What is the circumference of the
circle? (This would be the distance traveled by a passenger in one full
rotation of the Ferris wheel.)
Circumference = ________________________________________
13. 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?
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