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nlexa [21]
3 years ago
11

Ok so I found the area of a rectangle.

Mathematics
1 answer:
Kay [80]3 years ago
6 0

Answer:

  circle area = 1963.495 ft²

Step-by-step explanation:

<u>Given</u>

  A rectangle 550 ft by 350 ft packed with circles on a rectangular grid

<u>Find</u>

  the area of the largest circle that can be packed this way

<u>Solution</u>

The diameter of the circle must be a factor of both 350 and 550. We want the diameter to be the largest such factor. We can write the factors of 350 and 550 as ...

  • 350 = 50 × 7
  • 550 = 50 × 11

The largest factor common to both numbers is 50, so that will be the diameter of the largest circle that will fit on a square grid.

The area of a circle is commonly given by the formula ...

  A = πr² . . . . . where r represents the radius of the circle.

The radius is half the diameter, so will be (50 ft)/2 = 25 ft. And the area of the circle is ...

  A = π(25 ft)² = 625π ft² ≈ 1963.495 ft²

The area of one circle is about 1963.495 square feet.

_____

The total number of circles is 11×7 = 77. Their total area is 77×1963.495 ft² ≈ 151,189 ft². This is 151,189/192,400 ≈ 78.54% of the total area of the rectangle.

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