SOLUTION: Hi! I am having difficulty in answering our task in Math. The problem is about filling a pool with 1 000 cubic meters with conditions per pool. The following is the problem: Thi

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Question 912333: Hi! I am having difficulty in answering our task in Math. The problem is about filling a pool with 1 000 cubic meters with conditions per pool. The following is the problem:
Think as if you are a young engineer. Your task is to design a swimming pool that will hold a total of 1 000 cubic meters of water. Prepare 3 proposals to meet the following conditions:
• Pool A – a square with semicircles on each side, at least 1 meter deep.
• Pool B – a circle, at least ½ m deep
• Pool C – a rectangle with semicircles, at least 1.5 m deep
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
I will only help with pool A.

This one has the shape square as part of top and bottom but unknown depth. The semicircular four sides will be equivalent to TWO cylinders same depth as the rectangular or square part and same diameter as the side of the square part.

Volume of the square part of unknown depth h, side length of square x,
h%2Ax%5E2;
Volume of the two-cylinders part capping the four sides of the square part,
h%2Api%28x%2F2%29%5E2;

The question specifies h%3E=1, and then x is still unknown and needs to be solved. The volume is specified to be 1000 cubic meters.

Keeping both h and x as variable, potentially both unknown,
hx%5E2%2Bh%2Api%2A%28x%2F2%29%5E2=1000
hx%5E2%2Bh%2Api%2Ax%5E2%281%2F4%29=1000
highlight%284hx%5E2%2Bh%2Api%2Ax%5E2=4000%29
Starting h at the required minimum 1 meter,
4x%5E2%2Bpi%2Ax%5E2=4000
%284%2Bpi%29x%5E2=4000
x%5E2=4000%2F%284%2Bpi%29
highlight%28x=2sqrt%281000%29%2F%284%2Bpi%29%29
x=8.8559 meters as decimal approximation.
For measurement in practice, better to say 8.8 or 8.9 meters.

Pool C description is imprecise, or it may be intended as open-ended for a description. You are not restricted to an exactly known quantity of semicircles, and you have two UNKNOWN dimensions for the rectangular part. Pool C is not clearly enough described.