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MALAYAN COLLEGES

LAGUNA

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SOLID MENSURATION- CYLINDERS -

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MALAYAN COLLEGES LAGUNA

CYLINDER A cylinder  is a solid bounded by a

closed cylindrical surface and two

parallel planes.

Properties: 1. The bounding cylindrical surface

of a cylinder is called lateral surface,

and the two bounding planes are

called bases.

2. The bases of a cylinder are equal.

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CYLINDER

Properties: 3. The altitude of a cylinder is the

perpendicular distance between the

bases

4. The sections of a cylinder made by two

parallel planes, neither of which cuts a

base and both of which cut an element,

are congruent.

 

4

5. !ery section of a cylinder parallel to the base has an area

equal to that of the base.

". The section of a cylinder which contains an element of the

cylinder and a point of the cylindrical surface not in this point is aparallelogram.

#. The elements of a cylinder are equal.

$. A right section % of a cylinder is a section perpendicular to all

elements of the cylinder.

 

K 

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MALAYAN COLLEGES LAGUNA

CYLINDER&'()*+A-

 The !olume of a cylinder is equal either to the

product of a base and the altitude, or  to the

product of a right section and an element.

  Volume = Area of base x altitude

  V = Bh *   olume / right section 0 element

  V = Ke

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The lateral area of a cylinder is equal to theproduct of the perimeter of the right section and an element.

  S or  LSA = pK • e

* note: may apply to non-circular shapes 

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MALAYAN COLLEGES LAGUNA

CYLINDER

A right circular cylinder is a circular cylinderwhose elements are perpendicular to itsbase.

  For the Volume,

  V = Bh = πr2

h = π(d2

!"h  For the #ateral Area,

  #A (or $" = %& e = 2πrh = πdh

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CYLINDER

%'B#)*$+. -he aerage depth o/ a la&e is

estimated to be !0 /t. 1/ the sur/acearea is acres, 3nd the olume o/

water in the la&e. ( one acre =!4,50 s6. /t."

2. An indoor roller7s&ating rin& with an

area o/ ,00 s6. yard has a concrete8ooring 4 in. thic&. Find the amounto/ concrete used in laying the 8oor.

4. -he diameter o/ a well is 5 /t., and

the water is 9 /t. deep. :ow many 7

•

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CYLINDER

!. -he new :onda ity 200>,.) Variant has an engine( iV-), ! ales, ! cylinders" w9.40 cm. bore (diameter" and

;.>! cm. stro&e (length"declared that its capacity is.0#. Veri/y i/ the declaredcapacity is correct.

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CYLINDER. A paint manu/acturer desires a cylindricalsteel drum to hold 0 gal. o/ roo/ paint. Forconenience in handling, it is /ound necessaryto limit the inside diameter to 2 ? /t. Findthe height o/ the drum desired. ( ne gallon

= 24 cu. in."5. Find the waste in ma&ing the largestpossible cylindrical rod /rom a bar o/ iron 4 /t.long which has a s6uare cross section whose

diagonal is 5 in.9. A cubic /oot o/ water weighs about 52.!lbs. @hat must be the diameter o/ acylindrical pail /t. high in order /or it tohold the water /rom 2 lbs o/ water< :owmany s6uare inches o/ sheet tin are re6uired9

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CYLINDER>. A cylindrical standpipe is to contain

4!4,000 gallons o/ water. 1/ its height is tobe twice its diameter, what must be thedimensions<

0.

@hen a body is immersed in water in aright circular cylinder 50 cm. in diameter,the leel o/ the water rises !0 cm. @hat isthe olume o/ the body<

. -he coered water reseroir in a certaintown is ; m. high with a base diameter o/5 m. Find the olume o/ water it containswhen /ull in liters.

2. -he eterior o/ the reseroir in the

preious problem (Co. ", including the 10

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CYLINDER

4. A rectangle, 4 cm. wide and ; cm. long, isbeing reoled about its longer side. Find thetotal area and the olume o/ the cylindergenerated.

!. Determine the radius o/ a right circularcylinder i/ it has a lateral area o/ ;; s6. cm.and has a olume o/ 220 cu. cm.

. A metal washer in. in diameter ispierced by ? in. hole. @hat is the olume o/

the washer i/ it is ; in. thic&<

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MALAYAN COLLEGES LAGUNA

CYLINDER

A circular cylinder is a cylinder which has a circularright section.

  For the Volume,

V= Bh or

V = Ke

  For the #ateral Area,$ = %& e

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C=2πrB

h

 Lateral Surface(unrlle!"