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Sphere and hemisphere, solid and hollow sheet
5-mark answer frame

A hollow hemispherical bowl has outer radius 6 cm and inner radius 5 cm. Find its curved surface area, total surface area and the volume of material in it. (Take π = 3.14.)

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write what is given and what is to be found R = 6 cm, r = 5 cm. To find: CSA, TSA and the volume of material.
  2. 2 · Draw the figure Draw a semicircle for the outer edge and a smaller semicircle inside it with the same centre. Mark R = 6 cm and r = 5 cm, and shade the flat ring at the rim (1 cm wide).
  3. 3 · Write the formulas CSA = 2π(R² + r²); TSA = π(3R² + r²); volume = (2/3)π(R³ − r³).
  4. 4 · Find the curved surface area
    • CSA = 2 × 3.14 × (36 + 25)
    • = 6.28 × 61 = 383.08 cm²
  5. 5 · Find the total surface area
    • TSA = 3.14 × (3 × 36 + 25)
    • = 3.14 × 133 = 417.62 cm²
  6. 6 · Find the volume of material
    • V = 2/3 × 3.14 × (216 − 125)
    • = 2/3 × 3.14 × 91
    • = 571.48 ÷ 3 ≈ 190.49 cm³
  7. 7 · Check and box the answer CSA = 383.08 cm², TSA = 417.62 cm², volume ≈ 190.49 cm³ (rounded to two decimal places).

Scoring tip: For a hollow hemisphere, add the squares for the curved faces, 2π(R² + r²), but subtract the cubes for the volume, (2/3)π(R³ − r³).