Solid Mensuration Review

7/25/2019 Solid Mensuration Review

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SOLID MENSURATION


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Solids for which V=Bh


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PRISMS

WhereV = volue of !he "risAR= $re$ of !he ri%h! sec!io&

L = le&%!h of !he l$!er$l sideA

'= $re$ of !he '$se

h = $l!i!udeAL= $re$ of !he l$!er$l side

PR= "erie!er of !he ri%h! sec!io&

Note!h$! for ri%h! "ris( AR= A'$&d L = h)


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Rectangular Parallelepiped(Cuboid)

Cylinder


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Solids for which V=*+,-.Bh


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Re%ul$r Te!r$hedro&


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/RUSTRUM

hBbbBV3

)( ++=


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PRISMATOID

( ) hMbBV6

4++=


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S"here

22

33

4

243

4

DRS

DR

V

==

==


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( )

3

32

hRhV

=

( )6

33 222

hbah

V

++

=

3

ZR

V =


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RhZ 2=


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E$ch side of $ !e!r$dec$%o& is 0e1)

Wh$! is i!s $re$2$) 34)56 e3s7) u&i!s

') +6)-- e3s7) u&i!s

c) +8)-- e3s7) u&i!s

d) 56)-8 e3s7) u&i!s

e) &o&e of !hese


14/25

A cor&er lo! of l$&d is -8 o& o&e sides!ree! $&d 38 o& !he o!her s!ree!) The

$&%le 'e!wee& !he !wo li&es of !hes!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

$) Ph" +)


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A c:li&dric$l %$soli&e !$&>( l:i&%

hori?o&!$ll:( ;)


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Two ver!ic$l s7u$re ":r$id$l !$&>s *'o!hi&ver!ed. h$ve !heir ver!ices co&&ec!ed ': $shor! hori?o&!$l "i"e) O&e !$&> i&i!i$ll: full of

w$!er h$s $& $l!i!ude of +; fee! $&d $ '$seed%e of - fee!) The o!her !$&> i&i!i$ll: e"!:h$s $& $l!i!ude of ++ fee! $&d $ '$se ed%e of8 fee!) If w$!er is $llowed !o ow !hrou%h !he

co&&ec!i&% "i"e @&d !he level !o which !hew$!er will ul!i$!el: rise i& !he e"!: !$&>)*&e%lec! !he w$!er i& !he "i"e.

$) 6)3 fee!

') +6)4; fee!

c) )3 fee!

d) +)53 fee!

e) &o&e of !hese


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A !i& cu" is i& !he sh$"e of $ frus!u of$ co&e) The i&!er&$l di$e!ers of !he

cu" $! !he !o" $&d !he 'o!!o $reres"ec!ivel: - i&ches $&d 5 i&ches( $&d!he i&!er&$l de"!h is 6 i&ches) Su""ose!h$! $ co&ic$l "iece is $dded i&!o !hecu" so $s !o co"le!e !he co&e) /i&d !hevolue of !he co"le!e co&e)

$) -3C cu) i&ches

') -+C cu) I&chesc) --C cu) i&ches

d) -;C cu) i&ches

e) &o&e of !hese


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I! is desired !o cu! o $ "iece of le$d

"i"e 3 i&ches i& ou!side di$e!er $&d+,5 i&ches !hic>( so !h$! i! will el!i&!o $ co&e of di$e!er ++);884i&ches $&d $& $l!i!ude of 3 i&ches)

ow lo&% would !h$! "iece of le$d"i"e 'e2

$) -)44 fee!

') 56)86 fee!c) 3)44 fee!

d) 3;)68 fee!

e) &o&e of !hese


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/i&d !he u""er '$se ed%e of !he

frus!u of $ re%ul$r "e&!$%o&$l":r$id if i!s volue is +8;8)5++cu'ic e!ers( !he lower '$se ed%e is+; $&d !he $l!i!ude is +8 e!ers)

$) 8 e!ers

') 6 e!ers

c) e!ers

d) 5 e!ers

e) &o&e of !hese


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A %$llo& of w$!er is "oured i&!o $

s"heric$l 'owl of r$dius 8)3 i&ches)/i&d !he di$e!er of !he surf$ce of!he w$!er)

$) +;)35- i&ches

') +;)5-3 i&ches

c) +3)5-+ i&ches

d) ++)3-5 i&ches

e) &o&e of !hese


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A heis"heric$l !$&> co&!$i&s li7uids

A $&d B wi!h $ !o!$l de"!h of +3 c)wi!h li7uid B o& !o" of li7uid A) Li7uidA h$s $ de"!h of 4 c) If !he volueof li7uids A $&d B $re e7u$l) o"u!e

!he R$dius of !he !$&>)$) +5)6 c

') -)86 c

c) +3)85 cd) 34)5 c

e) &o&e of !hese


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To wh$! hei%h! us! $ $& 'e r$ised

$'ove !he e$r!h i& order !o see o&eFfour!h of i!s surf$ce2

$) h!) = r$dius of !he e$r!h

') h!) = di$e!er of !he e$r!h

c) h!) = h$lf of !he e$r!hGs r$dius

d) h!) = !wice !he r$dius

e) &o&e of !hese


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/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-


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A solid co&sis! of $ heis"here

surou&!ed ': $ co&e) /i&d !hever!ic$l $&%le of !he co&e if !hevolues of !he co&ic$l $&d s"heric$l"o!io&s $re e7u$l)

$) 8-9;4G

') 6-936G

c) 369-5G

d) -+95-G

e) &o&e of !hese


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Solve for !he Volue of !he

Pris$!oid

-;9

8 f!

- f!

Solid Mensuration Review

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