Soal dan Kunci Jawaban Test Matematika Kelas 9 , Menghitung Luas dan Volume

Tabung F
Lp = 2πr(r + t)
Lp = 2 x 22/7 x 3,5 (3,5 + 20)
Lp = 22 (23,5)
Lp = 517 dm⊃2;
V = πr⊃2;t
V = 22/7 x 3,5⊃2; x 20
V = 770 dm⊃3;

2. Panjang dari unsur tabung, yaitu:

Jawaban:

a. V = πr⊃2;t
t = V : (πr⊃2;)
t = 600π : (π x 10⊃2;)
t = 600π : (100π)
t = 6 cm

b. Lp = 2πr(r + t)
(r + t) = Lp : 2πr
(5 + t) = 120π : 2π5
(5 + t) = 120π : 10π
(5 + t) = 12
t = 12 - 5 = 7 cm

c. V = πr⊃2;t
t = V : (πr⊃2;)
t = 224π : (π x 4⊃2;)
t = 224π : (16π)
t = 14 m

d. Lp = 2πr(r + t)
(r + t)r = Lp : 2π
(r + 13)r = Lp : 2π
13r + r⊃2; = 528π : 2π
13r + r⊃2; = 264
r⊃2; + 13r - 264 = 0
(r + 24)(r - 11)
r = -24 atau r = 11, maka r = 11

e. Lp = 2πr(r + t)
(r + t)r = Lp : 2π
(r + 15)r = 450π : 2π
15r + r⊃2; = 450π : 2π
15r + r⊃2; = 225
r⊃2; + 15r - 225 = 0
r1 r2 = (-b ± √(b⊃2; - 4ac))/2a
r1 r2 = (-15 ± √((-15)⊃2; - 4x1x(-225))/2x1
r1 r2 = (-15 ± √(225 + 4x225))/2
r1 r2 = (-15 ± √(225 x5))/2
r1 r2 = (-15 ± 15√5))/2
r1 r2 = -15/2 + (15√5)/2
r = -15/2 + (15√5)/2

f. V = πr⊃2;t
r⊃2; = V : (πt)
r = √(V : (πt))
r = √(294π : (π6))
r = √49 = 7 m

3. Nilai 1/r + 1/t adalah sebagai berikut.

Jawaban:

r = r
t = t
r < t>V = V
Lp = L
V = πr⊃2;t
Lp = 2πr(r + t)
V = L
πr⊃2;t = 2πr(r + t)
rt = 2(r + t)
1/2 = (r + t)/rt
r/rt + t/rt = 1/2
1/t + 1/r = 1/2
Maka, ada kemungkinan nilai V = L jika 1/r + 1/t = 1/2 dan r < t>

4. a. Luas Permukaan Magnet

Jawaban:

L alas = L lingkaran besar - L lingkaran kecil
L alas = π(r2)⊃2; - π(r1)⊃2;
L alas = π x 6⊃2; - π x 4⊃2;
L alas = 3,14 x 36 - 3,14 x 16
L alas = 113,04 - 50,24 = 62,8 cm⊃2;
L selimut tabung besar = keliling x t
L selimut tabung besar = 2πr x t
L selimut tabung besar = 2 x 3,14 x 6 x 10
L selimut tabung besar = 376,8 cm⊃2;
L selimut tabung kecil = keliling x t
L selimut tabung kecil = 2πr x t
L selimut tabung kecil = 2 x 3,14 x 4 x 10
L selimut tabung kecil = 251,2 cm⊃2;
LP magnet = 2 L alas + L selimut tabung besar + L selimut tabung kecil
LP magnet = 2 x 62,8 + 376,8 + 251,2
LP magnet = 125,5 + 376,8 + 251,2
LP magnet = 753,8 cm⊃2;