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Single solids: the formulas you need sheet
3-mark answer frame

A cone has radius 5 cm and height 12 cm. Find its slant height, curved surface area and volume. (Use 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. Given r = 5 cm, h = 12 cm. To find: l, CSA and volume.
  2. 2 · Draw the figure. Draw a cone. Mark the radius r = 5 cm on the base. Show the height h = 12 cm as a dotted line from the tip to the centre. Mark the slant height l along the side.
  3. 3 · Write the formulas. l = √(r² + h²), CSA = πrl, volume = (1/3)πr²h.
  4. 4 · Find the slant height. l = √(25 + 144) = √169 = 13 cm.
  5. 5 · Find the CSA and the volume.
    • CSA = 3.14 × 5 × 13 = 204.1 cm².
    • Volume = (1/3) × 3.14 × 25 × 12 = 3.14 × 100 = 314 cm³.
  6. 6 · Check and box the answer. Units: cm for length, cm² for area, cm³ for volume. Box: l = 13 cm, CSA = 204.1 cm², volume = 314 cm³.

Scoring tip: Write each formula before you substitute. Examiners give a mark for the correct formula even if a later step slips.