A scanned copy of my notes reviewer in Solid Mensuration. Includes topics in Plane Mensuration.Full description
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Solid Mensuration. I had a hard time in my first year tracking this book, so here, world! :) Have a copy.Full description
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Notes on solid state
Geometry
SOLID SOLID MENSUR MENSURA ATION TION
Solids for which V=Bh
PRISMS •
Where V = volue of !he "ris AR = $re$ of !he ri%h! sec!io& L = le&%!h of !he l$!er$l side A' = $re$ of !he '$se h = $l!i!ude AL = $re$ of !he l$!er$l side PR = "erie!er of !he ri%h! sec!io& Note !h$! for ri%h! "ris( A R = A' $&d L = h)
Rectangular Parallelepiped (Cuboid)
Cylind er
Solids for which V=*+,-.Bh
Re%ul$r Te!r$hedro&
/RUSTRUM
V
=
( B + b + 3
Bb )
h
PRISMATOID
V
=
( B + b + 4 M ) 6
h
S"here
V
=
S =
4π R
3
3 4π R
2
D π =
3
24
D = π
2
V
V =
π h
2
=
( 3 R − h ) 3
ZR 3
V
π h
=
( 3a
2
+
3b
6
2
+
h
2
)
Z =
2π Rh
•
E$ch side of $ !e!r$dec$%o& is 0e1) Wh$! is i!s $re$2 $) ') c) d) e)
A cor&er lo! of l$&d is -8 o& o&e side s!ree! $&d 38 o& !he o!her s!ree!) The $&%le 'e!wee& !he !wo li&es of !he s!ree! 'ei&% 439) The o!her !wo li&es of !he lo! $re res"ec!ivel: "er"e&dicul$r !o !he li&es of !he s!ree!s) Wh$! is !he wor!h of !he lo! if i!s u&i! "rice is Ph" 3(8;; "er s7u$re e!er2 $) ') c) d) e)
Ph" +)<4 M Ph" 3)3-5 M Ph" +)844 M Ph" +)445 M &o&e of !hese
•
A c:li&dric$l %$soli&e !$&>( l:i&% hori?o&!$ll:( ;)<; e!ers i& di$e!er $&d - e!ers lo&% is @lled !o $ de"!h of ;)6 e!ers) ow $&: %$llo&s of %$soli&e does i! co&!$i&2 $) ') c) d) e)
A heis"heric$l !$&> co&!$i&s li7uids A $&d B wi!h $ !o!$l de"!h of +3 c) wi!h li7uid B o& !o" of li7uid A) Li7uid A h$s $ de"!h of 4 c) If !he volue of li7uids A $&d B $re e7u$l) o"u!e !he R$dius of !he !$&>) $) ') c) d) e)
+5)6 c -)86 c +3)85 c 34)5 c &o&e of !hese
•
To wh$! hei%h! us! $ $& 'e r$ised $'ove !he e$r!h i& order !o see o&eF four!h of i!s surf$ce2 $) ') c) d) e)
h!) = r$dius of !he e$r!h h!) = di$e!er of !he e$r!h h!) = h$lf of !he e$r!hGs r$dius h!) = !wice !he r$dius &o&e of !hese
•
/i&d !he $re$ of !he e$r!hGs surf$ce wi!hi& !he Arc!ic ircleH !h$! is( i& l$!i!ude &or!h of 669-3G N( !he $""roi$!e r$dius of !he e$r!h is -<6; iles) $) ') c) d) e)
