Lesson 5 MATH13-1

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Lesson 5 PYRAMIDS AND CONES

Solids for which V= Bh

Week

MA!"#$%#Solid Mens&r'(ion

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PYRAMID A pyramid is ' )ol*hedron

con('inin+ (ri'n+&l'r l'(er'l f'ceswi(h ' co,,on -er(e. 'nd ' /'sewhich is ' )ol*+on0

A )*r',id is ' right pyramid if (heline 1oinin+ (he -er(e. 'nd (he cen(erof /'se is )er)endic&l'r (o (he )l'ne

of (he /'se0 O(herwise2 (he )*r',idis s'id (o /e oblique0

If (he /'se of ' ri+h( )*r',id is '

re+&l'r )ol*+on (hen (he solid is s'idReference3 Solid Mens&r'(ion3 4nders('ndin+ (he $%D S)'ce /*

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A )*r',id is n',ed /* (he (*)e of)ol*+on in i(s /'se0

PYRAMID

O/li&e S&'reP*r',id

Pen('+on'lP*r',id

Reference3 Solid Mens&r'(ion3 4nders('ndin+ (he $%D S)'ce /*

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!he lateral surface area of aregular pyramidis e&'l (o h'lf (he)rod&c( of (he )eri,e(er of i(s /'se

'nd i(s sl'n( hei+h(0LSA= 6Pl

!o('l S&rf'ce Are'3TSA= B7 LSA

PYRAMID


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8ol&,e of P*r',id

V= Bh

where B= /'se 're' 9)ol*+on:0


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Rel'(ionshi)s A,on+ Al(i(&de2 Sl'n("ei+h(2 L'(er'l Ed+e 'nd (he ;'se


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CONE

A circular coneis ' cone whose /'seis

' circle0

!he axis of a circular coneis (he line se+,en( 1oinin+ (he

')e. 'nd (he cen(er of (he /'se0

If (he '.is is )er)endic&l'r (o(he /'se2 (he cone is '

right circular cone0


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A cone whose '.is is no()er)endic&l'r (o (he /'se is c'lledoblique0

4nless o(herwise s)eci

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S&rf'ce Are' of Cone

L'(er'l Are'3 LSA= rl

!o('l S&rf'ce Are'3 TSA= r>

7 rl


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8ol&,e of Cone

V= r>h


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E?AMPLES

@#2 )#>3 A re+&l'r he.'+on'l )*r',idh's one l'(er'l ed+e which ,e's&res #c,0 !he len+(h of one side of i(s /'se is

B c,0 ind (he 'l(i(&de 'nd (he sl'n(hei+h( of (he +i-en )*r',id0 Also

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@$2 )#$3 An in-er(ed s&'re )*r',id h's 'hei+h( e&'l (o F , 'nd ' (o) ed+e e&'l (o $,0 Ini(i'll*2 i( con('ins w'(er (o ' de)(h of 5 ,0

Wh'( is (he ini(i'l -ol&,e of (he w'(er in (he('nkG

If 'ddi(ion'l w'(er is (o /e )&,)ed in(o (he('nk '( (he r'(e of > +'llons )er ,in&(e2

how ,'n* ho&rs will i( ('ke (o

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E?ERCISES

50> E?ERCISES @>2 )#$3 A ri+h(circ&l'r cone h's ' l'(er'l 're' of#>F f(>'nd ' /'se 're' of 5#> f(>0

ind (he -ol&,e0

50> E?ERCISES @2 )#$3 A ri+h(

circ&l'r cone is inscri/ed in ' c&/eh'-in+ ' di'+on'l which ,e's&res#H$ c,0 ind (he -ol&,e of (he cone

'nd (he -ol&,e of s)'ce /e(ween (heReference3 Solid Mens&r'(ion3 4nders('ndin+ (he $%D S)'ce /*

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E?ERCISES

50> E?ERCISES @2 )#3 !he l'(er'led+e of ' re+&l'r he.'+on'l )*r',id is(wo (i,es (he len+(h of (he /'se ed+e0 If

(he ')o(he, of (he /'se is F c,2 0 c,$

50> E?ERCISES @2 )#3 If (hedi',e(er of (he /'se re,'ins cons('n(2/* wh'( f'c(or sho&ld (he 'l(i(&de /eReference3 Solid Mens&r'(ion3 4nders('ndin+ (he $%D S)'ce /*

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E?ERCISES

50> E?ERCISES @##2 )#3 W'(er isowin+ o&( of ' conic'l f&nnel (hro&+hi(s ')e. '( ' r'(e of #> c&/ic inches )er

,in&(e0 If (he f&nnel is ini(i'll* f&ll2 howlon+ will i( ('ke for i( (o /e one%(hird%f&llGWh'( is (he hei+h( of (he w'(er le-elGAss&,e (he r'di&s (o /e B inches 'nd(he 'l(i(&de of (he cone (o /e #5 inches0

ANS3 $#0 ,in2 #0 in


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"OMEWORJ 5

50# E?ERCISES3 @Ks #%/2 #%c2 2 #))0 #$#%#$>

50> E?ERCISES3 @Ks #2 $2 >$ ))0 #$%##


Lesson 5 MATH13-1

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