LECTURE 7 - CONE REV.pptx

8/19/2019 LECTURE 7 - CONE REV.pptx

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MALAYAN COLLEGES

LAGUNA



MALAYAN COLLEGES LAGUNA

SOLID MENSURATION

MATH 014

2




CONE

cone is a solid bounded by a conical surface (lateral

surface) whose directrix is a closed curve, and a plan

e (base) which cuts all the elements.

Properties:

1. The altitude of a cone is the perpendicular distance fr

om the vertex to the plane of the base.

. The axis of a cone is the strai!ht line "oinin! vertex wit

h the center of the base.

3

base

vertex




CONE

Properties

#. $very section of a cone made by

a plane passin! throu!h its verte

x % containin! two points of bas

e is a trian!le.

4

4. A right section of a cone is asection perpendicular to its

axis & cutting all theelements.

5. A circular cone is a conewhose right section is a

circle

rightsection

base




CONE

&ormula:

The volume of the cone is e'ual to onethir

d the product of the base and the altitude.

olum e * 1+# base x alt itude

* 1+# h

5

base

vertex




CONE

ri!ht circular cone is a circular cone whose a

xis is perpendicular to its base.

6

Properties:

1. The slant height of the

right circular cone is thelength of an element.

2. The altitude of a rightcircular cone is thedistance between the

ertex & the center of thecircle which forms its base.

!. All elements of a rightcircular cone are e"ual.




CONE

Properties:

-. ri!ht circular cone is a solid !en

erated by rotatin! a ri!ht trian!le

about one of its le!s as an axis.

http:++www.mathsisfun.com+!eometry+cone.html

. section of a ri!ht circular cone p

arallel to the base is a circle whos

e center is on the axis of the cone.

/. section of a ri!ht circular cone w

hich contains the vertex % two poi

nts of the base is an isosceles tria

n!le.

7

http://www.mathsisfun.com/geometry/cone.html

http://www.mathsisfun.com/geometry/cone.html




CONEP450$6

1. The crater of a volcano is app

rox. in the shape of a cone of ba

se #.1-1/ mi

. The crater7s dept

h is 188 ft. 9ow many cubic ya

rds of earth will be re'uired to fi

ll this cavity

( ns: 1./1; x 18

;

cu. yard ) (1mile* <8ft)

. pile of sand is in the form o

f a ri!ht circular cone of altitude

= ft. and slant hei!ht ft. >ha

t is the wei!ht of the sand, if the

sand wei!hs 18=. lbs + cu. ft. (

ns: -#,<;= lbs. )

#. 9ow many s'uare yards of ca

nvas will be re'uired to ma?e a

conical tent 1 ft. hi!h and 1< ft.

9

!#imagehere




CONE

P450$6

-. ri!ht circular cone of slant hei!ht 18 in. has a radi

us of - in. &ind the an!le, in de!rees, of the sector of a

circle of radius 18 in. whose area is e'ual to the lateral

area of the cone.

( ns: 1--

o

)

10




CONEP450$6

&ind the volume and the total surface area of

a ri!ht circular cone whose base radius is < c

m. and whose altitude is 1 cm.

( ns: #8

pi

cu. cm.A 88pi s'. cm. )

cylindrical tower #8 ft. in diameter has a co

nical roof the len!th of whose eaves is ft.

n element of the roof is inclined -

8

to

the horiBontal. &ind the weather surface

(rooftop).

( ns: 11;= s'. ft .)

piece of lead pipe of inner diameter C in.,

outer diameter of

+<

in., and len!th 1/ ft. h

as been melted in an open conical pot of radi

us 18 in and altitude 1 in. &ind the depth of

11




CONE

piece of lead pipe of inner diameter C i

n., outer diameter of +< in., and len!th

1/ ft. has been melted in an open conical p

ot of radius 18 in and altitude 1 in. &ind t

he depth of the molten metal

( ns: <.-8

in. )

olution:

ol pipe * = ./= cu .in.

=./= * 1 +# pi (r

)

h 18+1

* r+h

r * 18h+1

=./= * 1+# pi (18h+1 )

h

h

#

* =./=

1+# pi (18+1 )

h * <.#;< in

12

h

10

15

r

10 = r15 h



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