Surface Area — Solutions

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1. Q1 — Surface area of rectangular prisms

   Fluency
   • (a) SA = 2(lw + lh + wh) = 2(15 + 20 + 12) = 2 × 47 = 94 cm².
   • (b) SA = 2(96 + 72 + 48) = 2 × 216 = 432 cm².

2. Q2 — Surface area of cylinders

   Fluency
   • (a) SA = 2πr² + 2πrh = 50π + 100π = 150π ≈ 471.24 cm².
   • (b) SA = 2π(12.25) + 2π(28) = 24.5π + 56π = 80.5π ≈ 252.89 cm².

3. Q3 — Surface area of spheres

   Fluency
   • (a) SA = 4π(49) = 196π ≈ 615.75 cm².
   • (b) r = 7.5 m. SA = 4π(56.25) = 225π ≈ 706.86 m².

4. Q4 — Open cylinder (no lid)

   Understanding
   • SA = πr² + 2πrh = 16π + 72π = 88π ≈ 276.46 cm².

5. Q5 — Square pyramid

   Understanding
   • SA = l² + 2ls = 64 + 160 = 224 m².

6. Q6 — Cone with given perpendicular height

   Understanding
   • (a) l = √(36 + 64) = √100 = 10 cm.
   • (b) TSA = π(36) + π(6)(10) = 36π + 60π = 96π ≈ 301.59 cm².

7. Q7 — Hemisphere

   Understanding
   • (a) Curved SA = 2πr² = 2π(25) = 50π ≈ 157.08 cm².
   • (b) TSA = 2πr² + πr² = 3πr² = 75π ≈ 235.62 cm².

8. Q8 — Tin can manufacturing

   Understanding
   • (a) CSA = 2π(4)(12) = 96π ≈ 301.59 cm².
   • (b) Base area = π(16) = 16π ≈ 50.27 cm².
   • (c) Material per tin = 112π ≈ 351.86 cm². 100 000 cm² ÷ 351.86 = 284.2 → 284 complete tins.

9. Q9 — Composite solid: cylinder with hemisphere on top

   Problem Solving
   • Base circle + cylinder curved + hemisphere curved = 25π + 100π + 50π = 175π ≈ 549.78 cm².

10. Q10 — Painting a conical roof on a silo

    Problem Solving
    • (a) l = √(16 + 9) = √25 = 5 m.
    • (b) CSA_cone = π(4)(5) = 20π ≈ 62.83 m².
    • (c) CSA_cyl = 2π(4)(6) = 48π ≈ 150.80 m².
    • (d) Total = 20π + 48π = 68π ≈ 213.63 m².
    • (e) 213.63 ÷ 8 = 26.7 → round up to 27 litres.