Question 870959: How many full circles with a diameter of 2 feet can fit inside of a triangle with an area of 125,000 feet squared?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The area of a circle of radius  is  .
A circle with a diameter of 2 feet, has a radius of 1 foot.
So, it has a surface area (in square feet) of  .
Unless we are allowed to slice such circles into smaller pieces as needed to make them fit in the triangle, there is not enough information to solve the problem as written, because we do not know the shape of the triangle.
A triangle with an area of 125,000 square feet, could be long and narrow,
with a base measuring 2 feet and a height of 125,000 feet,
and there would be no way to get even 1 whole circle with a 2 feet diameter in such a triangle.
On the other hand, an isosceles triangle with a base measuring 1000 feet and a height of 250 feet, would also have a surface area of 125,000 square feet, and would fit many circles with 2 feet diameters.
If we are allowed to split our circles into pieces so as to be able to cover as much of the triangle's surface as possible, we could fit
 circles.
Since  , in that 125,000 square feet triangle,
we could fit 39,788 circles with 2 feet diameters (chopped into pieces as needed).
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