Question 1178876: the subzero community association is going to build a skating rink in a park. They have thirty 3-m-long sections of board that will be used to contain the rectangular rink
a)several different dimensions of the rink are possible. Give the dimensions of two possibilities
b) is the rink that has a length-to-width ratio of 2:1 possible? Explain.
c) is a square rink possible? explain
d) which rink has the greatest surface area? give its dimensions and justify your choice
e) the ice for the rink you found in part d) is to be 3cm thick, but it also needs to cover the wading pool that is used during the summer. This circular wading pool has a shallow cone shape with a diameter of 10 m and depth of 30 cm at the center. How much water will be required to initially flood this rink? round your answer to the nearest litre?
Answer by Solver92311(821)   (Show Source):
You can put this solution on YOUR website!
Presuming the number of boards on any side must be an integer, only the following dimensions are possible (excluding quarter-turn rotations):
Number of boards Meters
1 X 14 3 X 42
2 X 13 6 X 39
3 X 12 9 X 36
4 X 11 12 X 33
5 X 10 15 X 30
6 X 9 18 X 27
7 X 8 21 X 24
However, since you did not specify that the number of boards on a side had to be an integer, a square rink is possible if they were to saw two of the boards in half.
The greatest area of a rectangle with a given perimeter is a square. So, for an integer number of boards, it must be the dimensions that are closest to a square.
For part e, calculate the area in part d, and multiply by 0.03 meters (3 cm) to get the volume of the ice in the rink. For the wading pool, calculate the area of the upper surface and multiply by the depth at the center, then divide the result by 3. The volume of a cone is  where  is the area of the base.
John
My calculator said it, I believe it, that settles it
From
I > Ø
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