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Solids for WV=(1/Py
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CONE
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A cone is a solid bounded by a conical surfac
surface) hose directri! is a closed cur"e# an(base) hich
cuts all the ele%ents&
directrixbase
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'ro$erties
1& he altitude of a cone is the $er$endicular
distance fro% the "erte! to the $lane of the base&
*& E"ery section of a cone %ade by a $lane $assin+
throu+h its "erte! , containin+ to $oints of
base is a trian+le&
3& he a!is of a cone is the strai+ht line -oinin+
"erte! ith the center of the base&
.& A ri+ht section of a cone is a section $er$en
dicular to its a!is , cuttin+ all the ele%ents&
0& A circular cone is a cone hose ri+ht section is a
circle
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A ri+ht circular
cone
is a circula
r
cone hos
$er$endicular to its base&
'ro$erties1& he slant hei+ht of the ri+ht
circular
cone is the len+th of anele%ent&
*& he altitude of a ri+ht circular cone is
the
distance beteen the "erte! , thecenter
of the circle hich for%s its base&
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.& All ele%ents of a ri+htcircular cone are eual&
0& A section of a ri+ht circular cone
$arallel to the base is a circle
hose center is on the a!is of
the cone&2& A section of a ri+ht circular
cone hich contains the"erte! , to $oints of thebase is an
isosceles trian+le&
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FORMULAS
•
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TSA = area of
the
bas
e
+surfac
e
are
a
2
=πr +
πrl where
,
r is
the
radius
h is the height
l is the slant
height
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1& he crater of a "olcano is a$$ro!i%ately in
sha$e of a cone of base 3&1.12 s&
%ile&
he craters de
1044ft& 5o %any cubic yards of earth ill be re
6llthis ca"ity7
(1mile=5280ft)( Ans: 16.219 x 108 cu. yard )
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*& A $ile of sand is in the for% of a ri+ht
coneof altitude 8 ft& and slant hei+ht *0 ft& W
ei+ht of the sand# if
the
ft&7
sand ei+hs 14
cu&
Ans: 453,900 lbs.
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3& 5o %any suare yards of can"as ill be r
%a9e
a conical tent 10 ft& hi+h and 1: ft& in d14; of the
%aterial is asted7
( Ans: 61.061 sq. yd. )
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.& A ri+ht circular cone of slant hei+ht 14
has aradius of .
in&
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0&
