Pi Day - The Solutions
March 10, 2008

First find the area of the whole pie.

A = πr2

A = (3.14)(10/2)2 = 78.5 sq inches

Now multiply by the fraction of the pie that Wilma took.

78.5(60/360) = 13.1 square inches

First find the circumference of each of the wheels.

C = πd

C = (3.14)(12) = 37.68 inches

C = (3.14)(18) = 56.52 inches

Now convert the number of yards traveled by the buggy to inches.

300 yds (3 ft/yd) (12 in/ft) = 10800 inches

Divide the distance travelled (in inches) by the distance travelled in one revolution of each wheel.

10800/37.68 = 286.624

10800/56.52 = 191.083

Finally, find the difference.

286.624 - 191.083 = 95.5 revolutions, to the nearest tenth

If semicircle A’s radius is 10 cm, we know that B’s radius is 5cm and that C’s radius is 16.66667cm.

Now we can find the area of each semicircle.

A = (πr2)/2

A = (3.14)(10)2/2 = 157

A = (3.14)(5)2/2 = 39.25

A = (3.14)(16.66667)2/2 = 3935/9 or 436.1111…

Now find the sum.

(3935/9) + (157) + (39.25) = 22765/36 or 632.36111…

NOTE: your final answer may differ SLIGHTLY because of differences in rounding on this problem.

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