A Question of Watering
A farmer has
a plot of land in the shape of a square that is 100m on a side.
An irrigation system can be installed with the option of one large
circular sprinkler or nine small sprinklers, as shown below:
Please help farmer Euclid decide which plan will provide water to the greatest percentage of land in the field. (At this point we will not be considering cost of the systems and/or water usage).
Roping a Square
Given a square
of any size, stretch a rope tightly around it. Now take the rope
off, add 100ft to it and put the extended rope back around the
square so that the new rope makes a square around the original
square. Make sure there is uniform spacing between the original
square and the square formed by the rope. What is the distance
between a side of the original square and the corresponding side
of the rope square?
Slicing a Circle
A shaded region
is sliced off a circle when it is divided by a segment that has
endpoints on the circle.
What is the measure of the central angle of the circle that will make the shaded region's area 1/4 of the entire circle's area?
Dartboard Dilemma
Since Miss Sheehy
is an Olympic archer and a mathematician, she is fascinated by
the geometry of a dartboard/target. She is currently investigating
how the area of the outside shaded region compares with the area
of the inside shaded region (see p.619 in your text for shading
directions).
How do they compare??
On the Trail
You'll have to get this problem off the handout given out in class on Monday