In Circles!
Two circles are put next to each other, of the same radius.
Then, a thick material is wrapped tightly around the circles, leaving no gaps; except for where the highest and lowest points of the circles, which make two parallel lines (highlighted in red).
If the vertical height of the whole shape is , what is the area of the whole shape (including the material around the circles and the gaps)? (in cm)
The answer is 321.938040026.
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1 solution
Sorry! Thanks to everyone who spotted my error(s). It should be fine now.
Here’s @Joshua Lawrence Garcia ’s solution to the problem, rewritten slightly.
We need to split this up into two factors and rejoin them together: in this scenario we’ll split up the material around the circles into the colours which they already have been.
We can split up the circles into semi-circles, and add on the blue parts for 2 semi-circles radius 7 c m . 2 semi-circles equals 1 circle, so that part of the area is 4 9 π c m .
The middle part turns out to be a rectangle - we know its height is 1 4 c m , but it turns out that by using radii of the original circles, we find out that its length is 1 2 c m . Therefore, the middle rectangle’s area must be 1 6 8 c m .
1 6 8 + 4 9 π = 3 2 2 c m (to 3s.f.)