Mathemathic’s Assignment2

8/14/2019 Mathemathics Assignment2

1/21

MathemathicsAssignment

By:

Kevin Ansyari

Dyah Rusty Indriani

Listari Husna Fitri

Yuki Leonita


2/21

English Indonesia


3/21

The volume of a right circular cone is

given by the formula , where

is the radius of the base andis the height of the cone. If

, find, in terms of , the value of

and of so that the volume of the

cone is a maximum.

h

hrV2

3

1=

r)0( >=+ aahr

a r

h

QUESTIONS SHEET

Answer


4/21

A closed box with a square base is

to have a volume of 2000 cm3. Thematerial for the top and bottom of

the box costs $3 per m2, and the

material for the sides of the box

costs $1.50 per m2. What are the

dimensions of the box if the cost ofthe materials is to be a minimum?

Answer


5/21

Given that the volume of a right solid

cylinder of radius cm is, cm3

find the value of for which the total

surface of the solid is a minimum.

r 250

r

r

Answer


6/21

Answer of 1st Questions

Known :

The volume of a right circular cone =

. Radius = , height = .

Asked :

= ?

= ?

hrV2

3

1= r h

r

h

next


7/21

Answer of 1st Questions

hrV2

3

1=

ahr =+

rah =

hrV2

3

1=

)(3

1 2rarV =

32

3

1

3

1rarV =

0'max ==VV

03

2 2= rra

2

3

2rra =

ar3

2=

rah =

aah3

2=

ah3

1=

next


8/21

Answer of 2nd Questions

Known :

V = 2000 cm3

Cost for the top and bottom = $ 3 / m2

,Cost for the sides = $1.5 / m2

Asked:px lx t = ?

next


9/21

Answer of 2nd Questions

2000=V

txV2

=

tx22000 =

2

2000

xt =

5,1.43.2/Cost 22 xtxm +=

2

2 2000

.66)( xxxxB+=

xxxB

120006)( 2 +=

0)(' =xB

012000

122

=

xx

2

1200012

x

x =

10002 =x

10=x

2

2000

x

t=

100

2000=t

20=t

next

Minimun cost:

px lx t = 10x l0x 20


10/21

Answer of 3rd Questions

Known :

r =

V =

Asked :

Value of r = ?

r

250

next


11/21

Answer of 3rd Questions

home last

rr

rrr

rtr

r

V

5002

25022

22Surface Area

2

2

2

2

3

+=

+=

+=

rt 250

2=

tr2502

=

tV 2

=

cm250=

cm5

1255004

5004

0r

500-r4

0SA'minSA

3

3

2

2

=

=

=

=

=

==

r

r

r

rr


12/21

Volume sebuah kerucut sempurna di

berikan, dimana adalah jari-

jari alasnya dan adalah tinggikerucut. Jika temukan

dalam , nilai dan sehingga

volume kerucut maksimum.

h

hrV2

3

1= r

)0( >=+ aahr

a r

h

jawab

SOAL


13/21

Sebuah kotak tertutup beralas

persegi memiliki volume 2000 cm3.Bahan/materi untuk tutup dan alas

kotak seharga $3 per m2, dan

bahan/materi untuk sisi kotak

seharga $1.50 per m2. Apakah

dimensi kotak jika hargabahan/materinya harus minimum.

jawab


14/21

Diberikan volume silinder solid,

dengan jari-jarinya cm adalahcm3

temukan nilai supaya luas area

silinder harus minimum.

r

250r

r

jawab


15/21

Jawaban No. 1

Diketahui :

V =

r =h =

Ditanya := ?

= ?

hrV2

3

1=

r

h

r

h

lanjut


16/21

Jawaban No. 1

hrV2

3

1=

ahr =+

rah =

hrV2

3

1=

)(

3

1 2rarV =

32

3

1

3

1rarV =

0'max ==VV

03

2 2= rra

2

3

2

rra =

ar3

2=

rah =

aah3

2=

ah3

1=

lanjut


17/21

Jawaban No. 2

Diketahui :

V = 2000 cm3

Harga untuk atas dan alas = $ 3 / m2

,Harga untuk sisi-sisi samping = $1.5 / m2

Ditanya :px lx t = ?

lanjut


18/21

Jawaban No. 2

2000=V

txV2

=

tx22000 =

2

2000

xt =

5,1.43.2/Cost 22 xtxm +=

2

2 2000.66)(x

xxxB +=

x

xxB12000

6)( 2 +=

:minBiaya

0)(' =xB

012000

122

=

xx

2

1200012

xx =

10002 =x

10=x

2

2000

xt=

100

2000=t

20=t

lanjut


19/21

Jawaban No. 3

Diketahui :

r =

V =

Ditanya :

Nilai r = ?

r

250

lanjut


20/21

rr

rrr

rtr

rt

tr

trV

V

5002

25022

22PermukaanLuas

250

250

cm250

2

22

2

2

2

2

3

+=

+=

+=

=

=

=

=

cm5

125

5004

5004

0r

500-r4

0LP'minLP

3

3

2

2

=

=

=

=

=

==

r

r

r

rr

Jawaban No. 3

home last


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Mathemathic’s Assignment2