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Lesson 4 PRISMS AND CYLINDERS
Solids for which V= Bh
Week 6
MAT!"#!Solid Mens$r%&ion
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A prism is de'ned %s % (ol)hedronwi&h &wo con*r$en&
+%ses &h%& lie in
(%r%llel (l%nes, %nd whose e-er)sec&ion &h%& is
(%r%llel &o % +%se h%s&he s%.e %re% %s &h%& of
&he +%se/
Reference0 Solid Mens$r%&ion0 1nders&%ndin* &he "#D
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Aright prism is % (ris. whose l%&er%l f%ces
or l%&er%l ed*es %re (er(endic$l%r &o &he
&wo+%ses/
A regular prismis % ri*h& (ris. whose +%ses%re re*$l%r
(ol)*ons/ If &he +%se is % re*$l%r
(ol)*on of nsides &hen &he (ris. con&%ins nn$.+er of
con*r$en& l%&er%l f%ces which %rerec&%n*les/
An oblique prism is % (ris. whose l%&er%lf%ces or
l%&er%l ed*es %re no& (er(endic$l%r&o i&s +%ses/
I&s l%&er%l f%ces %re(%r%llelo*r%.s/
Reference0 Solid Mens$r%&ion0 1nders&%ndin* &he "#D
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A right section of % (ris. is %sec&ion .%de +) % (l%ne
(er(endic$l%r &o one of &he l%&er%led*es/
An oblique section is .%de +) %(l%ne o+li2$e &o one of
&he l%&er%led*es/
Reference0 Solid Mens$r%&ion0 1nders&%ndin* &he "#D
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S$rf%ce Are%s
The lateral area of a prismis &he(rod$c& of &he
(eri.e&er Pof % ri*h&sec&ion %nd &he len*&h eof
% l%&er%l
ed*e/LSA= Pe
Total Surface Area:
TSA= 3B LSAwhere Bis &he %re% of one +%se/
Reference0 Solid Mens$r%&ion0 1nders&%ndin* &he "#D
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5ol$.e of Pris.
V= BhV= Bh= Re
R= Bsin
Reference0 Solid Mens$r%&ion0 1nders&%ndin* &he "#D
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A rectangular solid, %lso known %srectangular parallelepiped is
%(ol)hedron wi&h &wo rec&%n*$l%r
+%ses %nd l%&er%l ed*es &h%& %re(er(endic$l%r &o
&he +%ses/
h
wl
Rec&%n*$l%r Solids
Reference0 Solid Mens$r%&ion0 1nders&%ndin* &he "#D
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Rec&%n*$l%r Solids
Di%*on%l 0
S$rf%ce Are%0 TSA= 3lw 3lh 3wh
5ol$.e0 V= lwh
Reference0 Solid Mens$r%&ion0 1nders&%ndin* &he "#D
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A cube is % he8%hedron whose !3ed*es %re %ll con*r$en&/
d
ss
s
C$+e
Reference0 Solid Mens$r%&ion0 1nders&%ndin* &he "#D
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C$+e
Di%*on%l0 d= 9" s
S$rf%ce Are%0 TSA= 6s3
5ol$.e0 V= s"
Reference0 Solid Mens$r%&ion0 1nders&%ndin* &he "#D
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A cylinder is &he solid +o$nded +) %closed c)lindric%l
s$rf%ce %nd &wo (%r%llel
(l%nes c$&&in* %ll &he ele.en&s of
&hes$rf%ce/
Acircular cylinderis one whose +%ses %recircles/ I& .%) %lso
+e &ho$*h& of %s %
(ris. wi&h &wo e2$%l circ$l%r +%ses/ A circ$l%r c)linder
is % right circular
cylinder, if &he hei*h& or &he line se*.en&
dr%wn &hro$*h &he cen&er of &he
+o&&o.+%se connec&s &he cen&er of &he
&o( +%se/:&herwise, &he c)linder is s%id &o
+eoblique/
Reference0 Solid Mens$r%&ion0 1nders&%ndin* &he "#D
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S$rf%ce Are%s
LSA= 3;rh TSA= 3B LSA
Reference0 Solid Mens$r%&ion0 1nders&%ndin* &he "#D
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5ol$.e of C)linder
V= ;r3h
V= Bh= Re
Reference0 Solid Mens$r%&ion0 1nders&%ndin* &he "#D
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E>0 The &ro$*h in &he '*$re h%s&r%(e?oid%l ends
which lie in (%r%llel (l%nes/
The &o( of &he &ro$*h is %
hori?on&%lrec&%n*le 6 f& +) !6 f& %nd &he
de(&h of &he
&ro$*h is 4 f&/%/ ow .%n) c$+ic fee& of w%&er
c%n i& hold@
+/ ow .%n) c$+ic fee& of w%&er does i&
con&%inwhen &he de(&h of &he w%&er is "
f&@
c/ Wh%& is &he %re% co-ered +) w%&er we&
(or&ionof &he con&%inerB wi&h &his
hei*h&@
ANS0 "3 f&", 33 f&", %nd !>!/" f&3/
Reference0 Solid Mens$r%&ion0 1nders&%ndin* &he "#D
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E
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The ri*h& sec&ion of % (ris. is in &hefor. of %
re*$l%r he8%*on whose%(o&he. .e%s$res c./ If &he
l%&er%l
%re% is "6 c.3
, wh%& is &he len*&h of&he l%&er%l ed*e of
&he (ris.@
ANS0 !/"> c.
Si.il%r e8%.(le fro. , (!3 wi&hdiFeren& *i-enB
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!, (!!60 A c)linder wi&h % -ol$.e ofG6; ." is circ$.scri+ed
%+o$& %s2$%re (ris. which h%s one side of &he
+%se &h%& .e%s$res ./ Wh%& is
&he%l&i&$de of &he c)linder@
ANS0 ! .
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6, (!G0 The len*&h of % rec&%n*$l%rsolid is &hree
&i.es &he wid&h %nd &hehei*h& is &wice
&he wid&h/ Hind &he
-ol$.e %nd &he len*&h of i&s di%*on%l if&he
&o&%l s$rf%ce %re% is !> in3/
ANS0 V= !63 in", d= !!/33 in
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4/! E
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4/" E
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:MEW:R 4
4/! E, !G ((/ !3#!4
4/3 E
