Volume Bola Yang Berdiameter 40 Cm Adalah

Volume Bola Yang Berdiameter 40 Cm Adalah

1. Tentukan volume sebuah kubus yang memiliki rusuknya 6 m!

Jawaban








V



=

r

3








=
6
m
×


6
m
×


6
m






=
216

m

3








{\displaystyle {\begin{aligned}V&=r^{3}\\&=6m\times 6m\times 6m\\&=216m^{3}\\\end{aligned}}}

2. Tangki air berbentuk balok memiliki panjang 3 m, lebar 80 cm, dan tingginya 60 cm. Tentukan volume tangki dalam satuan liter!

Jawaban








V



=
p
×


l
×


t






=
3
m
×


80
c
m
×


60
c
m






=
300
c
m
×


80
c
m
×


60
c
m






=
24.000
c

m

2


×


60
c
m






=
1.440.000
c

m

3








=
1.440
l






{\displaystyle {\begin{aligned}V&=p\times l\times t\\&=3m\times 80cm\times 60cm\\&=300cm\times 80cm\times 60cm\\&=24.000cm^{2}\times 60cm\\&=1.440.000cm^{3}\\&=1.440l\\\end{aligned}}}

3. Tentukan volume tabung dengan diameter 14 cm dan tinggi 21 cm!

Jawaban








d



=
14
c
m

 maka

r
=
7
c
m




V



=
π


×



r

2


×


t






=


22
7


×


7
c
m
×


7
c
m
×


21
c
m






=
3.234
c

m

3








{\displaystyle {\begin{aligned}d&=14cm{\text{ maka }}r=7cm\\V&=\pi \times r^{2}\times t\\&={\frac {22}{7}}\times 7cm\times 7cm\times 21cm\\&=3.234cm^{3}\\\end{aligned}}}

4. Tentukan volume kerucut yang berjari-jari 18 cm dan tinggi 10 cm!

Jawaban








V



=


1
3


×


π


×



r

2


×


t






=


1
3


×


3.14
×


18
c
m
×


18
c
m
×


10
c
m






=
3
,
391.2
c

m

3








{\displaystyle {\begin{aligned}V&={\frac {1}{3}}\times \pi \times r^{2}\times t\\&={\frac {1}{3}}\times 3.14\times 18cm\times 18cm\times 10cm\\&=3,391.2cm^{3}\\\end{aligned}}}

5. Tentukan volume prisma segitiga sisi dengan panjang sisi alas 10 cm dan tingginya 15 cm!

Jawaban








t
1



=



10

2






5

2




c
m






=


5


3




c
m






=
8.66
c
m




V



=


1
2


×


a
×


t
1
×


t
2






=


1
2


×


10
c
m
×


8.66
c
m
×


15
c
m






=


1
2


×


1
,
299
c

m

3








=
649.5
c

m

3






a
t
a
u




V



=


1
2


×


a
×


a
×


s
i
n
α


×


t






=
×




1
2


×


10
c
m
×


10
c
m
×


s
i
n
60
×


15
c
m






=


1
2


×


1
,
299
c

m

3








=
649.5
c

m

3








{\displaystyle {\begin{aligned}t1&={\sqrt {10^{2}-5^{2}}}cm\\&={\sqrt {5{\sqrt {3}}}}cm\\&=8.66cm\\V&={\frac {1}{2}}\times a\times t1\times t2\\&={\frac {1}{2}}\times 10cm\times 8.66cm\times 15cm\\&={\frac {1}{2}}\times 1,299cm^{3}\\&=649.5cm^{3}\\atau\\V&={\frac {1}{2}}\times a\times a\times sin\alpha \times t\\&=\times {\frac {1}{2}}\times 10cm\times 10cm\times sin60\times 15cm\\&={\frac {1}{2}}\times 1,299cm^{3}\\&=649.5cm^{3}\\\end{aligned}}}

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6. Tentukan volume limas persegi dengan panjang sisi alas 10 cm dan tingginya 12 cm!

Jawaban








V



=


1
3


×



s

2


×


t






=


1
3


×


10
c
m
×


10
c
m
×


12
c
m






=
4
c
m
×


100
c

m

2








=
400
c

m

3








{\displaystyle {\begin{aligned}V&={\frac {1}{3}}\times s^{2}\times t\\&={\frac {1}{3}}\times 10cm\times 10cm\times 12cm\\&=4cm\times 100cm^{2}\\&=400cm^{3}\\\end{aligned}}}

7. Tentukan volume bola yang berdiameter 40 cm! Jari-jari = 20cm

Jawaban








d



=
40
c
m

 maka

r
=
20
c
m




V



=


4
3


×


π


×



r

3








=


4
3


×


3.14
×


20
c
m
×


20
c
m
×


20
c
m






=


4
3


×


25.120
c

m

3








=
33
,
493.34
c

m

3








{\displaystyle {\begin{aligned}d&=40cm{\text{ maka }}r=20cm\\V&={\frac {4}{3}}\times \pi \times r^{3}\\&={\frac {4}{3}}\times 3.14\times 20cm\times 20cm\times 20cm\\&={\frac {4}{3}}\times 25.120cm^{3}\\&=33,493.34cm^{3}\end{aligned}}}

8. Tentukan volume kerucut terpancung jika diameter alasnya 10 dm, diameter atas 4 dm, dan tinggi 4 dm!

Jawaban








d
1



=
10
d
m

 maka

r
1
=
5
d
m




d
2



=
4
d
m

 maka

r
2
=
2
d
m




V



=


1
3


×


π


×


(
r

1

2


+
r
1
×


r
2
+
r

2

2


)
×


t






=


1
3


×


3.14
×


(
5
d
m
×


5
d
m
+
5
d
m
×


2
d
m
+
2
d
m
×


2
d
m
)
×


4
d
m






=
4.18
d
m
×


(
25
+
10
+
4
)
d

m

2








=
4.18
d
m
×


39
d

m

2








=
163.02
d

m

3








{\displaystyle {\begin{aligned}d1&=10dm{\text{ maka }}r1=5dm\\d2&=4dm{\text{ maka }}r2=2dm\\V&={\frac {1}{3}}\times \pi \times (r1^{2}+r1\times r2+r2^{2})\times t\\&={\frac {1}{3}}\times 3.14\times (5dm\times 5dm+5dm\times 2dm+2dm\times 2dm)\times 4dm\\&=4.18dm\times (25+10+4)dm^{2}\\&=4.18dm\times 39dm^{2}\\&=163.02dm^{3}\\\end{aligned}}}

9. Tentukan volume bola terpancung jika jari-jari alas 10 dm, jari-jari atas 7 dm dan tinggi 14 dm!

Jawaban








V



=


1
6


×


π


×


(
r

1

2


+
r

2

2


+

t

2


)
×


t






=


1
6


×




22
7


×


(
10
×


10
+
7
×


7
+
14
×


14
)
d

m

2


×


14
d
m






=
7.33
d
m
×


(
100
+
49
+
196
)
d

m

2








=
7.33
d
m
×


345
d

m

2








=
2
,
528.85
d

m

3








{\displaystyle {\begin{aligned}V&={\frac {1}{6}}\times \pi \times (r1^{2}+r2^{2}+t^{2})\times t\\&={\frac {1}{6}}\times {\frac {22}{7}}\times (10\times 10+7\times 7+14\times 14)dm^{2}\times 14dm\\&=7.33dm\times (100+49+196)dm^{2}\\&=7.33dm\times 345dm^{2}\\&=2,528.85dm^{3}\\\end{aligned}}}

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10. Berapa volume pipa berongga dengan diameter masing-masing 10 mm dan 18 mm serta tinggi 3.5 cm! (dalam mm persegi)

Jawaban








d
1



=
10
m
m

 maka

r
1
=
5
m
m




d
2



=
18
m
m

 maka

r
2
=
9
m
m




t



=
3.5
c
m
=
35
m
m




V



=
π


×


(
r

2

2





r

1

2


)
×


t






=


22
7


×


(
9
×


9



5
×


5
)
m

m

2


×


35
m
m






=
110
m
m
×


(
81



25
)
m

m

2








=
110
m
m
×


56
m

m

2








=
6
,
160
m

m

3








{\displaystyle {\begin{aligned}d1&=10mm{\text{ maka }}r1=5mm\\d2&=18mm{\text{ maka }}r2=9mm\\t&=3.5cm=35mm\\V&=\pi \times (r2^{2}-r1^{2})\times t\\&={\frac {22}{7}}\times (9\times 9-5\times 5)mm^{2}\times 35mm\\&=110mm\times (81-25)mm^{2}\\&=110mm\times 56mm^{2}\\&=6,160mm^{3}\\\end{aligned}}}



Volume Bola Yang Berdiameter 40 Cm Adalah

Sumber: https://id.wikibooks.org/wiki/Soal-Soal_Matematika/Volume_bangun_ruang

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