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2021-09-01, 02:10   #749
EdH

"Ed Hall"
Dec 2009

2×29×71 Posts

Quote:
 Originally Posted by xilman 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

2021-09-01, 02:23   #750
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

2×23×137 Posts

Quote:
 Originally Posted by EdH 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.

2021-09-01, 11:29   #751
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

1103310 Posts

Quote:
 Originally Posted by EdH 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.

2021-09-01, 12:51   #752
EdH

"Ed Hall"
Dec 2009

2·29·71 Posts

Quote:
 Originally Posted by EdH Perhaps I'm confused as well. . . .
Yep!
Quote:
 Originally Posted by retina Reading the alt text might help to explain. Geometry textbooks always try to trick you by adding decorative stripes and dotted lines.
Quote:
 Originally Posted by xilman 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. . .)

2021-09-01, 12:59   #753
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

2·23·137 Posts

Quote:
Ignore all of the internal lines and stripes (the "decorations") and just consider the area of the outer shape.

2021-09-01, 13:09   #754
EdH

"Ed Hall"
Dec 2009

2·29·71 Posts

Quote:
 Originally Posted by retina 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.

2021-09-01, 13:20   #755
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

11×17×59 Posts

Quote:
 Originally Posted by EdH 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.

2021-09-01, 14:25   #756
EdH

"Ed Hall"
Dec 2009

2·29·71 Posts

Quote:
 Originally Posted by xilman 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.)

 2021-12-07, 13:24 #757 firejuggler     "Vincent" Apr 2010 Over the rainbow 268510 Posts Nordic countries have the most impressive tourism add.

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