The diagram is formed from 6 identical closed -packed circles. If the height of the figure is 2 feet, find the radius of each circle in inches.
Diameter = 2/6 = 1/3 Ft. = 4 in.
Radius = 1/2 * 4 = 2 In.
Include your complete solution please.
There are 6 identical circles; the radius of each circle is 2 in.
To find the radius of each circle, we first need to convert the height of the figure from feet to inches, since we need the units to be consistent.
Given that 1 foot is equal to 12 inches, multiplying the height of the figure (2 feet) by 12 will give us the height in inches:
2 feet * 12 inches/foot = 24 inches
Now, let's consider the diagram formed from 6 identical closed-packed circles. If we draw a vertical line through the center of the diagram, we can see that the height of each circle is equal to the radius of a circle plus the diameter of another circle:
Height of the figure = Radius + Diameter
Since all the circles in the diagram are identical, the height of the figure is equal to the sum of the height of three circles:
Height of the figure = 3 * Height of one circle
Substituting the known values:
24 inches = 3 * Height of one circle
To find the height of one circle, divide both sides of the equation by 3:
Height of one circle = 24 inches / 3 = 8 inches
We know that the height of one circle is equal to the radius plus the diameter, so we can write:
8 inches = Radius + Diameter
Since the circles in the diagram are closed-packed, the diameter of a circle is equal to twice the radius:
8 inches = Radius + 2 * Radius
8 inches = 3 * Radius
To find the radius, divide both sides of the equation by 3:
Radius = 8 inches / 3 ≈ 2.67 inches
Therefore, the radius of each circle in the diagram is approximately 2.67 inches.