lectures 7 - solids (v=bh).pptx

7/25/2019 Lectures 7 - Solids (V=bh).pptx

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Solids for Which V

Rectangular Paralle

Circular C

Right Circular C


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Solid

Any three-dimensional bounded by surfaces or p

gures.


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Some examples of Solid Figures


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VO!"#S A$% S!&FA'# AA

VO!"# of a solid is the amount o

occupies.!nits of cubic length (cm)* m)* in)+.

S!&FA'# AA is the area of

dimensional surface.

!nits of surface area (cm,* m,* in,+.

SO%S


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A#&A S!&FA'# AA A$% OA S!&FA'# AA/

ateral Surface area/

otal Surface area/

area1

area2

arearea4

area5

area6

A) 0 A1 0 A2 0

A3A4 0 A, 0 A) 0 A1 0 A2 0A3

SO%S


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5&S"S


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A5&S" is a polyhedron of 6hich t6o faces are e7uin parallel planes* and the other faces are parallelogr

SO%S


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Properties:

4. he bases are the e7ual polygons8the lateral area is the sum of the

areas of the remaining faces.,. he altitude is the perpendiculardistance bet6een the planes of itsbases.

). A right section (9+ of a prism is a

section perpendicular to the lateraledges.

1. he intersections of the lateralfaces are called the lateral edges (e+.

e

5risms


9/485risms

Properties:

2. A right prismis a prism 6hoselateral edges are perpendicular toits bases8 its lateral faces arerectangles..

3. he sections of a prism made

by parallel planes cutting alllateral edges are e7ual polygons


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FORMULAS:

he :olumeof a prism is e7ualto the product of the area ofthe base and the altitude*

Volume = base x altitude

V = Bh.

e

B

5risms


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FO&"!AS/

he :olume of a prism is e7ual

to the product of a right sectionand a lateral edge.

Volume = right section x

lateral edge

V = Ke.

e

B

5risms FO&"!AS


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FO&"!AS/

he lateral area of a prism is e7ualproduct of the perimeter 5 of a right and the length e of a lateral edge

SA = 5e

e

5risms


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FO&"!AS/he total surface of a prism is e7ual

product of a lateral edge and the perimthe right section plus t6ice the areabase.

otal surface Area /SA = ,;0SA; is the area of one base

5risms


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A formula that works for all prisms, regardless of the base shape is as follows:


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5&O;#"S/

4. Write a formula for (a+ the :olume* (b+ theof a right prism 6hose altitude is h and 6hos

s7uare of edge a.

,. A lead pencil 6hose ends are hexagons 6a cylindrical piece of 6ood* 6ith the least 6original piece 6as < in. long and in. in dia

the :olume of the pencil.

5risms


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5&O;#"S/

). he base of a right triangular prism is a right tlegs are ,1 m. and ), m. respecti:ely. f the lateralis 41 m.* 6hat is the total area of the prism>

( Ans: 2,112 sq.m. )

5risms


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5&O;#"S/

1. A masonry dam 1? ft. high has a uniform :section. he dam is 1 ft. 6ide at the top* 4? ft.bottom and is


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PROBLEMS:

2. he lateral surface of a concrete octagonalpier of height 4? ft. is to be resurfaced. f each ofthe base edges is 4 ft.* ho6 many s7uare feet of

surfacing 6ill be re7uired>

( Ans: 80 sq. t. )

3. One part of a 7uart crystal is a hexagonalprism 6ith a right section of 4.,B s7. in.* and anedge of ,.)4 in.* and a base of 4.14 s7. in. Find

the altitude of the prism.( Ans: 2.11!4 in. ) e

5risms


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PROBLEMS:

C. he lateral area of a prism is 11< s7. m. f the la

C m.* 6hat is the perimeter of the right section>

( Ans: "4 m. )


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5&O;#"S/

B. A trench is 4


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PROBLEMS:

44. Find the :olume of 6ater in a s6imming pool ends and sides. he length measured at the 6ater and the breath is ,? ft. he bottom of the s6immiplane sloping gradually do6n6ard so that the d6ater at one end is 1 ft. and the other end is < ft.

( Ans: ",000 #u. t. )

4,. What are the dimensions of a gallon can of unicross section 6hose height is t6ice the length ofthe base> (One gallon = ,)4 cu. in.+

( Ans: 4.8& in. x .&4 in.)

5risms


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PROBLEMS:

4). An irrigation canal is ,?? m. long and , m. dee

6ide at the top and 4 m. at the bottom. Findexca:ated to maEe the canal.

( Ans: "00 #u. m.)

41. A trough* 6hose ends are isosceles right trianglesaxis* is 3 m. long. f it contains 42? of 6ater* ho6

6ater> ( 4 m) = 4??? +( Ans: 0.1" m.)

5&S"S

5risms


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5&O;#"S/

42. he trough sho6n in the gure has triangular enin parallel planes. he top of the trough is a horion

,? in. by )) in.* and the depth of the trough is 43 many gallons of 6ater 6ill it hold> (b+ Do6 many gacontain 6hen the depth of the 6ater is 4? in.> (c+ depth of the 6ater 6hen the trough contains ) gal.> 6etted surface 6hen the depth of 6ater is B in. ( O,)4 cu. in. +( Ans: 22.8" *al, 8.! *al, '.80 in., 801 sq. in.)

5risms


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5risms


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5risms


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5risms


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5risms


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5risms


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5risms


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'!;# A '!;# i l h d h i f


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A '!;# is a polyhedron 6hose six fall s7uares.

+%oe%ties:

1. he three dimensions of a cube are e

each other. 2. All the faces of a cube are congruent

'!;#


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LATERAL SURFACE AREA, LSA (CUBE)

SA cube= 1a,

TOTAL SURFACE AREA, TSA (!"e)

SA cube= 3a,

a

V cube= a)

#$%!&e (CUBE)

'!;#


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' a

'!;# 5&O;#" S#/


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4. Do6 much material is neededmanufacture of ,1 ??? celluloid

each die has an edge of G in

,. Sho6 that (a+ the total surface acube is t6ice the s7uare of its d(b+ the :olume of the cube is ticube of its diagonal.

'!;# 5&O;#" S#/


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). One cube has a face e7ui:alent to theof another cube. Find the ratio of their

'!;#

1 Find the :olume and total are5&O;#" S#/


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1. Find the :olume and total arelargest cube of 6ood that canfrom a log of circular cross

6hose radius is 4,.C inches.

'!;#

2 Wh t th l t l d5&O;#" S#/


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2. What are the largest :olume andarea of a cube that may be inscribinside a sphere 6hose :olume e7u

cu. in.>

'!;#


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&ectangular 5arallelepiped A 'A$H!A& 5A&A##55


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polyhedron 6hose six facerectangles.

&ectangular 5arallelepiped %AHO$A #$HD OF A'A$H!A& SO%


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'A$H!A& SO%

l

6

h

&ectangular 5arallelepiped S!&FA'# AA OF A 'A$H!A&SO%


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SO%

LATERAL SURFACE AREA, LSA

LSA 2 h * 2 h%TOTAL SURFACE AREA, TSA

TSA 2 h * 2 h% * 2%

&ectangular 5arallelepiped

l

6

h

VO!"#OF A 'A$H!A&SO%


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Vparallelepiped = l

- h


SO%

l

6

h

Properties of Rectangular Parallelepiped:


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p g p p

The parallel edges are equal.

The opposite lateral faces are equal and paral

Any two opposite faces maybe taken as the ba

&ectangular 5arallelepiped 5&O;#" S#/


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4. he length of a rectangular solid is ttimes the 6idth and the height t6ice tFind the :olume and the length of its d

the total surface area is

5&O;#" S#/


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,. Find the area of the triangular sectrectangular solid sho6n in the gure.

4

8

12

3+ ha- ./ -he e.h- $ -he /-ee%


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+ ha- / -h h- $ -h /-ee- %$, 4 ee- .'e a' 58 .h -he /-ee% e.h/ 475 $!'/ er !".

4+ .e -he $%!&e $ a r


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ara%%e%e.e' a/ 810 !". &e-er+ '.&e/.$/ . -he are . -he ra-.$ 2:3:5

lectures 7 - solids (v=bh).pptx

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