# 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

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

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

{\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}}}

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

{\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}}}

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

{\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}}}

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

{\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}}}

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

{\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}}}

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

{\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}}}

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

{\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}}}

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

{\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}}}

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

{\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}}}

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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