Tentukan luas permukaan dan volume dari bangun kerucut berikut


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Tentukan luas permukaan dan volume dari bangun kerucut berikut

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Latihan 5.2 Kerucut. 1. Tentukan luas permukaan dan volume dari bangun kerucut berikut.

Pendahuluan

Kerucut adalah limas yang bidang alasnya berbentuk lingkaran.

Rumus Kerucut

\boxed {V = \frac{1}{3} \times \pi \times r^{2} \times t}

\boxed {LP =\pi r (r + s)}

Panjang garis pelukis ⇒ s² = r² + t²

Pembahasan

  • a. r = 4 cm dan t = 12 cm

Luas permukaan kerucut

s² = r² + t²

   = 4² + 12²

   = 16 + 144

   = 160

s = √160

s = 4√10 cm

LP = π r (r + s)

    = π 4 (4 + 4√10) cm²

   = π × 4 × 4 (1 + √10) cm²

   = 16 π (1 + √10) cm²

   = 16 × 3,14 (1 + 3,16) cm²

   = 50,24 × 4,16 cm²

   = 209 cm²

Volume kerucut

V = \displaystyle \frac{1}{3} π r² t

  = \displaystyle \frac{1}{3} × 3,14 × 4 × 4 × 12 cm³

  = 3,14 × 16 × 4 cm³

  = 200,96 cm³

  • b. r = 6 cm dan s = 10 cm

Luas permukaan kerucut

LP = π r (r + s)

    = 3,14 × 6 (6 + 10) cm²

    = 18,84 × 16 cm²

    = 301,44 cm²

Volume kerucut

s² = r² + t²

10² = 6² + t²

100 = 36 + t²

t² = 100 - 36

t² = 64

t = √64

t = 8 cm

V = \displaystyle \frac{1}{3} π r² t

  = \displaystyle \frac{1}{3} × 3,14 × 6 × 6 × 8 cm³

  = 3,14 × 2 × 48 cm³

  = 301,44 cm³

  • c. r = 6 cm dan t = 10 cm

Luas permukaan kerucut

s² = r² + t²

s² = 6² + 10²

s² = 36 + 100

s² = 136

s = √136

s = 11,66

LP = π r (r + s)

    = 3,14 × 6 (6 + 11,66) cm²

    = 18,84 × 17,66 cm²

    = 332,71 cm²

Volume kerucut

V = \displaystyle \frac{1}{3} π r² t

   = \displaystyle \frac{1}{3} × 3,14 × 6 × 6 × 10 cm³

   = 3,14 × 2 × 60 cm³

   = 376,8 cm³

  • d. r = 7 cm dan s = 25 cm

Luas permukaan kerucut

LP = π r (r + s)

    = \displaystyle \frac{22}{7} × 7 (7 + 25) cm²

    = 22 × 32 cm²

    = 704 cm²

Volume kerucut

s² = r² + t²

25² = 7² + t²

625 = 49 + t²

t² = 625 - 49

t² = 576

t = √576

t = 24 cm

V = \displaystyle \frac{1}{3} π r² t

  = \displaystyle \frac{1}{3} × \displaystyle \frac{22}{7} × 7 × 7 × 24 cm³

  = 22 × 7 × 8 cm³

  = 1232 cm³

  • e. t = 3 cm dan s = 4 cm

Jari-jari

s² = r² + t²

4² = r² + 3²

16 = r² + 9

r² = 16 - 9

r² = 7

r = √7

r = 2,64 cm

Luas permuakaan kerucut

LP = π r (r + s)

    = 3,14 × 2,64 (2,64 + 4) cm²

    = 8,29 × 6,64 cm²

    = 55 cm²

Volume Kerucut

V = \displaystyle \frac{1}{3} π r² t

  = \displaystyle \frac{1}{3} × \displaystyle \frac{22}{7} × √7 × √7 × 3 cm³

  = \displaystyle \frac{22}{7} × 7 × 1 cm³

  = 22 cm³

  • f. r = 5 cm dan s = 13 cm

Luas permukaan kerucut

LP = π r (r + s)

    = 3,14 × 5 (5 + 13) cm²

    = 15,7 × 18 cm²

    = 282,6 cm²

Volume kerucut

s² = r² + t²

13² = 5² + t²

169 = 25 + t²

t² = 169 - 25

t² = 144

t = √144

t = 12 cm

V = \displaystyle \frac{1}{3} π r² t

  = \displaystyle \frac{1}{3} × 3,14 × 5 × 5 × 12 cm³

  = 3,14 × 25 × 4 cm³

  = 314 cm³

---------------------------------------------------------------------

Pelajari Lebih lanjut Tentang Bangun Ruang Sisi Lengkung

  1. Volume kerucut dan setengah bola → brainly.co.id/tugas/9364101
  2. Volume tabung diluar kerucut → brainly.co.id/tugas/14432299
  3. Luas permukaan bandul → brainly.co.id/tugas/4906
  4. Latihan 5.1 no 1 dan 2, luas permuaan volume dan panjang dari unsur tabung → brainly.co.id/tugas/4330490
  5. Sisa pasir dari wadah 1/2 bola dan kerucut → brainly.co.id/tugas/14763168

Detil Jawaban

  • Kelas        : 9 SMP
  • Mapel       : Matematika
  • Bab           : 5 - Bangun Ruang Sisi Lengkung
  • Kode         : 9.2.5

#AyoBelajar

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