Question

select the correct answer from each drop down menu. an office buys a break room table that is designed as four overlapping circles. how much space is available for use on this table? the radius of each circle is approximately 4 feet, and the area of each circle is approximately 50 square feet. together, with the area filled in between the circles, the table is approximately 200 square feet.

Explanation:

Step1: Find circle radius

The total width is 8 ft, which equals 2 radii.
$r = \frac{8}{2} = 4$ ft

Step2: Calculate area of 1 circle

Use circle area formula $A_{circle} = \pi r^2$.
$A_{circle} = \pi (4)^2 = 16\pi \approx 50.27$ square feet

Step3: Calculate total table area

The shape is equivalent to 3 full circles (the overlapping central area is covered by the 4 circles, so total area = 3×area of 1 circle).
$A_{total} = 3 \times 50.27 \approx 150.8$ square feet, or using exact terms: $A_{total}=3\times16\pi=48\pi\approx151$ square feet. (Note: The incorrect 200 overcounts overlaps, the 4 ft was a wrong radius guess, 50 is just one circle)

Answer:

The radius of each circle is approximately 4 feet, and the area of each circle is approximately 50 square feet. Together, with the area filled in between the circles, the table is approximately 151 square feet.