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8/14/2019 Mathemathics Assignment2
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MathemathicsAssignment
By:
Kevin Ansyari
Dyah Rusty Indriani
Listari Husna Fitri
Yuki Leonita
8/14/2019 Mathemathics Assignment2
2/21
English Indonesia
8/14/2019 Mathemathics Assignment2
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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
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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
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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
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Answer of 1st Questions
Known :
The volume of a right circular cone =
. Radius = , height = .
Asked :
= ?
= ?
hrV2
3
1= r h
r
h
next
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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
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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
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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
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Answer of 3rd Questions
Known :
r =
V =
Asked :
Value of r = ?
r
250
next
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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
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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
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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
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Diberikan volume silinder solid,
dengan jari-jarinya cm adalahcm3
temukan nilai supaya luas area
silinder harus minimum.
r
250r
r
jawab
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Jawaban No. 1
Diketahui :
V =
r =h =
Ditanya := ?
= ?
hrV2
3
1=
r
h
r
h
lanjut
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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
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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
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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
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Jawaban No. 3
Diketahui :
r =
V =
Ditanya :
Nilai r = ?
r
250
lanjut
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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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