Hi everyone, saw this 1 year old meme about "The Evolution of Education" being shared around lately.
It's quite a spicy jab at the sorry current state of the North American education system.
However, the geometry problem from the "1970s" caught my eye. So I made a video on how to solve it.
1970: Calculate the surface area of the object. (0:24)
At first glance, this object looks strange and there doesn't seem to be any recognizable formula for a shape's area to represent it.
But after some inspection, we see that this is just circles and rectangles and the differences of their areas.
The concave areas where the radius R is 10 and 5 are just what's left left behind when you intersect 2 circles into a rectangle's corners.
The circles where the radius is 4 is slightly trickier. You'd just have to imagine a circle being placed at the corner of a rectangle and the corner tip that is not overlapping with the circle is then removed. Don't worry we will have diagrams on this later.
Let's recolor this figure. The problem then boils down to removing the red areas from the rectangle to find the Area of the object.
If we refactor the problem some more, we now see that there are 3 components: a rectangle, 2 quarter circles (where radii are 10 and 5) and the 2 corner areas formed by square and circle where radius is 4.
Here's the formulas we will be using to solve this problem.
Area of Rectangle is Length x Width
Area of Circle is pi r squared (where pi is approximately 3.14159265)
Area of square is length of side squared
The area of rectangle is simply: 20 x 30 = 600
The area of a quarter circle is 1/4 pi r squared.
We see that the first quarter circle's area is 25pi, while the second is 6.25pi
So the combined area of the 2 red quarter circles is 31.25pi.
The area of 1 of the red corners is the difference of square and circle areas divided by 4 (since there are 4 corners).
From the diagram we see that the square has a side length of 8 since it spans the diameter of the circle. Diameter is 2 * radius.
The Area of both red corners is therefore:
2 * Area of one red corner, which after substituting 4 for radius and 8 for length, becomes 32 - 8pi
Putting it all together we have: Area of red quarter circles and corners removed from the Area of the rectangle:
600 - 31.25 pi - (32 - 8 pi) = 568 - 23.25 pi (Approx. ~ 494.957971) [EDIT: Video approximation is incorrect/less accurate]
From 1985 to 2015: Find the area of the rectangle (3:18)
No, the answer is not Michael Jackson, Canada, Breakfast, 800K or 4K.
From the previous problem, we know that the area of a rectangle is simply length x width:
The answer is therefore: 30 x 20 = 600.
2018: Color the rectangle with the color you prefer (3:41)
After I color a rectangle blue, I am cheered by people of all ages and showered in medals/trophies/fireworks.
Thanks for watching.
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#MATH #MATHFORFUN #EDUCATION
