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Surface area when a part is stuck on or cut out sheet
3-mark answer frame

From a solid cylinder of height 12 cm and radius 5 cm, a cone of the same height and radius is hollowed out. Find the total surface area of the remaining solid. (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; the cone has the same r and h. To find: the TSA of the remaining solid.
  2. 2 · Draw the figure. Draw the cylinder. Inside it, draw a dotted cone with its base on the top circle and its tip at the centre of the bottom. Mark r, h and l.
  3. 3 · Write the formula. TSA left = CSA of cylinder + area of bottom circle + CSA of cone = 2πrh + πr² + πrl.
  4. 4 · Find the slant height. l = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.
  5. 5 · Substitute. TSA = π(2 × 5 × 12 + 5 × 5 + 5 × 13) = π(120 + 25 + 65) = 210π.
  6. 6 · Work out the value. TSA = 210 × 3.14 = 659.4 cm².
  7. 7 · Check and box the answer. The top circle was removed, so it is not counted. Box: TSA = 659.4 cm².

Scoring tip: Name each surface in words before you use symbols. It earns the method mark even if the arithmetic slips.