Hemispheres for the Dummy Geometry Student

Hemisphere 

Here at the Antisocial Network, our research staffers charitably think that at least some of the freelance dumbassery they uncover is merely failure to understand the topics they attempt to cover. That doesn't release the writers from incurring the full wrath of the DotD, of course... In some cases, thought, we realize that the writer thought he or she was correct -- but just didn't completely think the topic through. That's what we suspect happened with today's candidate, Alexis Kezirian, as the eHow contributor answered... or thought she answered "How to Calculate the Surface Area of a Hemisphere."¹ Alexis' problem? A lack of critical thinking skills...

Kezirian begins, as eHowians are wont, by defining the terms of the question:

"A hemisphere is, essentially, half of a sphere. Surface area is the total exposed area of an object. "

So far, so good, although that "essentially" is superfluous. Alexis also provided -- e.g., googled, found, and reworded -- the formula for the surface area of a hemispherical dome:

"The equation for the surface area of a hemisphere is 2πr^2 (where the symbol ^ represents that the number following it is an exponent)... "

...which we find rather insulting to anyone hoping to calculate the surface area of a sphere – but apparently Alexis didn't know what the caret meant, so she "shared." You may wonder why she didn't explain what "π" is, but just be patient... Whatever the case, Alexis got it partially right: the surface area of a complete sphere is 4πr², and half of that is 2πr²: So did Alexis get it right? Well, no: If Alexis has been asked to calculate the volume of a hemisphere and used this approach, she'd have been right. The volume of a sphere is 4/3 πr³, and exactly half of that is 2/3 πr³ – the volume of a hemisphere. But what Kezirian forgot is that a hemisphere has two surfaces: a dome that is half a sphere and a circle that forms the base. So the total surface area of a hemisphere is the sum of the area of the dome (2πr²) and the area of the circular base (πr²): 3πr² !

It's an exercise in logic. Alexis failed, as we suspected she would when we saw the way in which she described the necessary calculations:

"The surface area of a hemisphere is calculated by deducing the area of the flat, circular base of the object (πr^2) and then multiplying this number by two..."

...and described a hemisphere's radius:

"Determine the radius of the hemisphere by measuring the distance from the exact center on its flat side upwards to the very height of its shape..."

...both of which make it abundantly clear that she knows nothing about the topic -- especially that "very height of its shape" bull. First, you don't "deduce" the area of a circle, and second, the radius of a hemisphere can be measured from the center of the base to any point on the curved surface. Alexis either didn't know this or wouldn't argue the point with a moronic eHow content editor (we know, redundant). That's all we need to name her our Dumbass of the Day... again.

¹ The original has been deleted by Leaf Group, but can still be accessed using the Wayback machine at archive.org. Its URL was    ehow.com/how_6223381_calculate-surface-area-hemisphere.html

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