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Learning Math Home
Measurement Session 7: Circles and pi
Session 7 Part A Part B Homework
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Session 7 Materials:

Session 7

Problem H1


A circle is inscribed in a square. What percentage of the area of the square is inside the circle?

Take it Further

Problem H2


Imagine that a giant hula hoop is fitted snugly around the Earth's equator. The diameter of the hula hoop is 12,800 km. Next, imagine that the hula hoop is cut and its circumference is increased by 10 m. The hula hoop is adjusted around the equator so that every part of the hula hoop lies the same distance above the surface of the Earth. Would you be able to crawl under it? Walk under it standing upright? Drive a moving truck under it? Determine the new diameter of the hoop, and find out the distance between the Earth and the hula hoop.



Problem H3


A new car boasts a turning radius of 15 ft. This means that it can make a complete circle with a radius of 15 ft. and return to its original spot. The radius is measured from the center of the circle to the outside wheel. If the two front tires are 4.5 ft. apart, how much further do the outside tires have to travel than the inside tires to complete the circle?

Take it Further

Problem H4


Your dog is chained to a corner of the toolshed in your backyard. The chain measures 10 ft. in length. The toolshed is rectangular, with dimensions 6 ft. by 12 ft. Draw the picture showing the area the dog can reach while attached to the chain. Compute this area.

Draw a diagram of the shed and the possible areas that the dog could reach on its chain. Then divide the space into different sections and calculate the area of each section.   Close Tip


Problem H5


An annulus is the region bounded by two concentric circles.


If the radius of the small circle is 10 cm and the radius of the large circle is 20 cm, what is the area of the annulus?


A dartboard has four annular rings surrounding a bull's-eye. The circles have radii 10, 20, 30, 40, and 50 cm. How do the areas of the annular rings compare? Suppose a dart is equally likely to hit any point on the board. Is the dart more likely to hit in the outermost ring or inside the region containing the bull's-eye and the two innermost rings? Explain.

Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Express the areas in terms of and then compare them.   Close Tip



Problem H6


An oval track is made by erecting semicircles on each end of a 50 m-by-100 m rectangle. What is the length of the track? What is the area of the region enclosed by the track?

Suggested Reading:

Zebrowski, Ernest (1999). A History of the Circle (pp. 48-49). Piscataway, N.J.: Rutgers University Press.
Reproduced with permission from the publisher. 1999 by Rutgers University Press. All rights reserved.

Download PDF File:
A History of the Circle

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