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Old 2021-09-01, 02:10   #749
EdH
 
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Originally Posted by xilman View Post
So?

The formula is a correct expression for the area of the figure depicted.
Perhaps I'm confused as well. Are not three of the four formulas depicting volume?

Edit: I suppose you could call volume A if you wanted to. . .

Last fiddled with by EdH on 2021-09-01 at 02:15
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Old 2021-09-01, 02:23   #750
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Quote:
Originally Posted by EdH View Post
Are not three of the four formulas depicting volume?
Reading the alt text might help to explain.

Geometry textbooks always try to trick you by adding decorative stripes and dotted lines.
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Old 2021-09-01, 11:29   #751
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Quote:
Originally Posted by EdH View Post
Perhaps I'm confused as well. Are not three of the four formulas depicting volume?

Edit: I suppose you could call volume A if you wanted to. . .
No, all depict areas.

Simple dimensional analysis shows that the formulae all denoted areas. All products of lengths contain precisely two factors.
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Old 2021-09-01, 12:51   #752
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Quote:
Originally Posted by EdH View Post
Perhaps I'm confused as well.
. . .
Yep!
Quote:
Originally Posted by retina View Post
Reading the alt text might help to explain.


Geometry textbooks always try to trick you by adding decorative stripes and dotted lines.
I had read it. It hadn't helped.
Quote:
Originally Posted by xilman View Post
No, all depict areas.

Simple dimensional analysis shows that the formulae all denoted areas. All products of lengths contain precisely two factors.
My limited analysis was to see "h" in the formulae. (I almost used this plural the first time, but, alas. . .)
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Old 2021-09-01, 12:59   #753
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Yep!I had read it. It hadn't helped.
Ignore all of the internal lines and stripes (the "decorations") and just consider the area of the outer shape.
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Old 2021-09-01, 13:09   #754
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Quote:
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Ignore all of the internal lines and stripes (the "decorations") and just consider the area of the outer shape.
Thank you - surface area of 3-D object, rather than volume of 3-D object! I was kind of thinking something wasn't quite correct for volume in the third example with pi*r/2.
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Old 2021-09-01, 13:20   #755
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Thank you - surface area of 3-D object, rather than volume of 3-D object! I was kind of thinking something wasn't quite correct for volume in the third example with pi*r/2.
close, but no cigar.

None of the objects depicted are three-dimensional. They are just flat shapes annotated with superfluous lines, etc, to fool you into thinking that they represent 3-D objects.

The "cuboid" for instance, is just a rectangle with a rhombus adjoined to two of its sides. The "cone" is a triangle adjoined to a segment of a circle, and so on.
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Old 2021-09-01, 14:25   #756
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Quote:
Originally Posted by xilman View Post
close, but no cigar.

None of the objects depicted are three-dimensional. They are just flat shapes annotated with superfluous lines, etc, to fool you into thinking that they represent 3-D objects.

The "cuboid" for instance, is just a rectangle with a rhombus adjoined to two of its sides. The "cone" is a triangle adjoined to a segment of a circle, and so on.
I see it now (he says again). I've flattened all the figures and taken into account the ellipses and b being half the triangle base for the second. I "think" I now have it!

Thank you for the help. (And, especially, for pointing out that I must take the time to fully look at these to appreciate them.)
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