• Luas seluruh permukaan = 390π cm² = 1224,6 cm².
• Volume = 9.180π cm³ = 28.825,2 cm³.

Pembahasan

Dua Kerucut Sepusat

Kerucut besar (1):

• Diameter: D = 24 cm.
  Jari-jari: R = 12 cm.
• Tinggi: T = 16 cm.
• Panjang garis pelukis:
  S = √(R² + T²) = √(12² + 16²)
  S = √(144 + 256) = √400
  S = 20 cm.

Kerucut kecil (2):

• Jari-jari: r = ¼·R.
• Tinggi: t = ¼·T.
• Panjang garis pelukis: s = ¼·S.

Luas seluruh permukaan

LP = LS1 + LS2 + LA1 – LA2
LP = π·(RS + rs + R² – r²)
LP = π·[RS + (¼·R)·(¼·S) + R² – (¼·R)²]
LP = π·[RS + (1/16)RS + R² – (1/16)R²]
LP = π·[(17/16)RS + (15/16)R²]
LP = π·[(17/16)·12·20 + (15/4²)·12²]
LP = π·[17·3·5 + 15·3²]
LP = π·[255 + 135]
LP = 390π cm²
(π = 3,14)
LP = 390·(3,14) cm²
LP = 1224,6 cm².

Volume

V = V1 – V2 = (π/3)(R³·T – r³·t)
V = (π/3)[R³T – (¼·R)³·¼·t]
V = (π/3)[R³T – (1/256)·R³T]
V = (π/3)·(255/256)·R³T
V = π·(85/256)·12³·16
V = π·(85/256)·(2²·3)³·2⁴
V = π·(85/2⁸)·2¹⁰·3³
V = π·85·4·3³ = π·340·27
V = 9.180π cm³
(π = 3,14)
V = 9.180·(3,14) cm³
V = 28.825,2 cm³.