Question

question: 3 six identical circles fit inside the rectangle as shown below. if the rectangle has a width of 15 units and a height of 10 units, what is the radius of each circle? image of a rectangle with 6 identical circles (3 in a row, 2 rows) inside, labeled with height 10 units and width 15 units options: 15 units, 10 units, 5 units, 2.5 units

Explanation:

Step1: Analyze the arrangement of circles

Looking at the diagram, we can see that there are 2 rows of circles and 3 columns of circles. The height of the rectangle (10 units) is equal to the diameter of 2 circles (since there are 2 circles stacked vertically). The width of the rectangle (15 units) is equal to the diameter of 3 circles (since there are 3 circles placed horizontally). Let's first use the height to find the diameter of one circle.

Step2: Find the diameter from the height

Since there are 2 circles vertically, the height of the rectangle (10 units) is equal to 2 times the diameter (\(d\)) of one circle. So we have the equation:
\(2d = 10\)
To find \(d\), we divide both sides by 2:
\(d=\frac{10}{2}=5\) units.

Step3: Find the radius from the diameter

The radius (\(r\)) of a circle is half of its diameter. So we use the formula \(r = \frac{d}{2}\). We know \(d = 5\) units, so:
\(r=\frac{5}{2}=2.5\) units.

We can also verify using the width. The width of the rectangle (15 units) is equal to 3 times the diameter of one circle. So \(3d = 15\), which gives \(d=\frac{15}{3}=5\) units, and then \(r=\frac{5}{2}=2.5\) units.

Answer:

2.5 units