Find the diameter of one circle

In summary, the given figure consists of five identical semicircles, where the diameter of one circle is to be found. After analyzing the figure, it can be deduced that the diameter is equal to the sum of the gaps between the semicircles, which is 36.
  • #1
anemone
Gold Member
MHB
POTW Director
3,883
115
Five identical semicircles are arranged as shown. Find the diameter of one circle.
[TIKZ]
\draw (0,0) -- (16.5, 0);
\begin{scope}
\clip (0,0) rectangle (4.5,4.5);
\draw (2.25,0) circle(2.25);
\draw (0,0) -- (4.5,0);
\end{scope}
\begin{scope}
\clip (6,0) rectangle (10.5,4.5);
\draw (8.25,0) circle(2.25);
\draw (6,0) -- (10.5,0);
\end{scope}
\begin{scope}
\clip (12,0) rectangle (16.5,4.5);
\draw (14.25,0) circle(2.25);
\draw (12,0) -- (16.5,0);
\end{scope}
\begin{scope}
\clip (2.75,0) rectangle (7.25,-4.5);
\draw (5,0) circle(2.25);
\draw (2.75,0) -- (7.25,0);
\end{scope}
\begin{scope}
\clip (9.25,0) rectangle (13.75,-4.5);
\draw (11.5,0) circle(2.25);
\draw (9.25,0) -- (13.75,0);
\end{scope}
\draw [<->] (4.5, 0.5) -- (6, 0.5);
\draw [<->] (10.5, 0.5) -- (12, 0.5);
\draw [<->] (0, -0.5) -- (2.75, -0.5);
\draw [<->] (7.25, -0.5) -- (9.25, -0.5);
\draw [<->] (13.75, -0.5) -- (16.5, -0.5);
\coordinate[label=left:12] (A) at (5.5,0.8);
\coordinate[label=left:12] (B) at (11.5,0.8);
\coordinate[label=left:22] (C) at (1.6,-0.8);
\coordinate[label=left:16] (D) at (8.6,-0.8);
\coordinate[label=left:22] (D) at (15.6,-0.8);
[/TIKZ]

As this is a Singapore primary math problem, it is understandable that one can solve it without the use of algebra method (form an equation and solve the equation is what I mean by algebra method). I enjoyed this problem quite a bit, therefore I wanted to post it here to let others to try to solve it without the use of algebra method...:)
 
Mathematics news on Phys.org
  • #2
I would say that the sums of the gaps are 24 (above) and 60 (below). As there is one more semicircle above, its diameter is equal to the difference 36.
 
  • #3
Thanks castor28 for your reply!

But, I still count that as an algebra method, hehehe...I will let others have a chance to take a stab at it before I post the so called without-algebra solution. Please stay tuned! :)
 
  • #4
Hi castor28!

I don't know where my head was when I made the previous reply (Tmi) , I'm so sorry!(Sadface) Your answer is spot on!

Here is a diagram to illustrate a slightly different approach than castors28's method:

[TIKZ]
\draw (0,0) -- (16.5, 0);
\begin{scope}
\clip (0,0) rectangle (4.5,4.5);
\draw (2.25,0) circle(2.25);
\draw (0,0) -- (4.5,0);
\end{scope}
\begin{scope}
\clip (6,0) rectangle (10.5,4.5);
\draw (8.25,0) circle(2.25);
\draw (6,0) -- (10.5,0);
\end{scope}
\begin{scope}
\clip (12,0) rectangle (16.5,4.5);
\draw (14.25,0) circle(2.25);
\draw (12,0) -- (16.5,0);
\end{scope}
\begin{scope}
\clip (0,0) rectangle (4.5,-4.5);
\draw (2.25,0) circle(2.25);
\draw (0,0) -- (4.5,0);
\end{scope}
\begin{scope}
\clip (12,0) rectangle (16.5,-4.5);
\draw (14.25,0) circle(2.25);
\draw (12,0) -- (16.5,0);
\end{scope}
\draw [<->] (4.5, 0.5) -- (6, 0.5);
\draw [<->] (10.5, 0.5) -- (12, 0.5);
\draw [<->] (4.5, -0.5) -- (6, -0.5);
\draw [<->] (7.25, -0.5) -- (9.25, -0.5);
\draw [<->] (10.5, -0.5) -- (12, -0.5);
\draw [<->] (6, -0.5) -- (7.25, -0.5);
\draw [<->] (9.25, -0.5) -- (10.5, -0.5);
\coordinate[label=left:12] (A) at (5.5,0.8);
\coordinate[label=left:12] (B) at (11.5,0.8);
\coordinate[label=left:12] (C) at (5.5,-0.8);
\coordinate[label=left:16] (D) at (8.6,-0.8);
\coordinate[label=left:12] (D) at (11.5,-0.8);
\coordinate[label=left:10] (E) at (6.9,-0.8);
\coordinate[label=left:10] (F) at (10.1,-0.8);
[/TIKZ]

$\therefore \text{diameter}=10+16+10=36$
 

1. What is the formula for finding the diameter of a circle?

The formula for finding the diameter of a circle is d = 2r, where d represents the diameter and r represents the radius.

2. How do I find the diameter of a circle if I only know the circumference?

To find the diameter of a circle if you only know the circumference, you can use the formula d = c / π, where d represents the diameter, c represents the circumference, and π is approximately 3.14.

3. Can I use a ruler to measure the diameter of a circle?

No, a ruler is not an accurate tool for measuring the diameter of a circle. You will need to use a compass or a measuring tape to get an accurate measurement.

4. Is the diameter of a circle always equal to twice the radius?

Yes, the diameter of a circle is always equal to twice the radius. This is a fundamental property of circles.

5. How do I find the diameter of a circle if I only know the area?

To find the diameter of a circle if you only know the area, you can use the formula d = √(4A / π), where d represents the diameter, A represents the area, and π is approximately 3.14.

Similar threads

Replies
10
Views
1K
  • General Math
Replies
2
Views
1K
  • General Math
Replies
2
Views
970
  • Poll
  • General Math
Replies
1
Views
2K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
996
  • MATLAB, Maple, Mathematica, LaTeX
Replies
3
Views
4K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
5K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
3K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
3K
Back
Top