Geometry Forum - Problem of the Week
Solutions - Circles and Semicircles, Dec. 6-10, 1993
Dan Hirschhorn
____________________Since ratio of diameters from semicircle to circle is 2:1, by Fund. thm of Similarity, area of Full circle to inscribed circle is 4:1 so area of semicircle to inscribed circle is 2:1. Thus inscribed circle takes up1/2 semicircle! Area of outside half = area of inscribed circle = 36 .
---
Daniel B. Hirschhorn | ISU Mathematics
danh@math.ilstu.edu | (309) 438-7849
Jonathan Jacobs
____________________
Explanation, eh? Well, let's see ...
One-half of a circle at radius 12 has area:
(1/2)pi(12)^2 or 72pi
The complete circle at diameter 12, radius 6 has area:
pi(6)^2 or 36pi
So, subtracting the smaller, inscribed circle from the larger
semicircle gives us:
72pi - 36pi, or _36 pi_.
Now do I get full credit, or is it too late? (Honest ... I had the
workthere originally, but I erased it ...)
-Jon (pigpen@hardy.u.washington.edu)
Nick Szmyd
____________________
Date: Wed, 15 Dec 93 15:35:35 -0500
To: pow@mathforum.org
Subject: puzzle of the week
I am a student at Shaler Area High School and have
been working on the puzzle of the week for December 6-10. I used
pi r squared to find the area of the circle which is 113 units. I used
pi r squared divided by two to find the area of the semicircle which
I found to be 226 units. I then subtracted the two areas to find the
area of the semicircle outside of the circle and I found that to be
113 units. Therefore, I have came to the conclusion that the area of
the semicircle outside the of circle is eqaul to the area of the
circle.
Previous page || Next problem || Table of Contents || Forum Home Page