Question

How many non-overlapping circles with an area of 817 can fit within a 37 by 55 rectangle?

A) 1
B) 2
C) 3
D) 4

Answer 1

To determine the number of non-overlapping circles with an area of 817 that can fit within a 37 by 55 rectangle, divide the area of the rectangle by the area of the circle.

Step-by-step explanation:

To determine the number of non-overlapping circles with an area of 817 that can fit within a 37 by 55 rectangle, we need to calculate the area of both the circle and the rectangle and then divide the area of the rectangle by the area of the circle. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. Given that the area of the circle is 817, we can solve for the radius:

817 = πr^2

r^2 = 817/π

r ≈ √(817/π)

Now, we can calculate the area of the rectangle:

Area of rectangle = length x width = 37 x 55 = 2035

Finally, we can divide the area of the rectangle by the area of the circle:

Number of circles = floor(2035/(A/π))