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Surface area of a combination of two solids sheet
3-mark answer frame

A wooden toy is a cone on a hemisphere, both of radius 6 cm. The total height of the toy is 14 cm. Find its total surface area and the cost of painting it at ₹ 5 per 10 cm². (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 = 6 cm, total height = 14 cm, rate = ₹ 5 per 10 cm². To find: surface area of the toy and the cost of painting.
  2. 2 · Draw the figure. Draw the hemisphere below and the cone on top. Show the hidden joining circle dotted. Mark r = 6 cm, the cone height h and the slant height l.
  3. 3 · Write the formula. Surface area of toy = CSA of cone + CSA of hemisphere = πrl + 2πr². The joining circle is hidden.
  4. 4 · Find the cone's height and slant height. h = 14 − 6 = 8 cm. l = √(36 + 64) = √100 = 10 cm.
  5. 5 · Substitute. Surface area = 3.14 × 6 × 10 + 2 × 3.14 × 36 = 188.4 + 226.08 = 414.48 cm².
  6. 6 · Find the cost. Cost = (414.48 ÷ 10) × ₹ 5 = ₹ 207.24.
  7. 7 · Check and box the answer. Only the curved surfaces were added. Box: surface area = 414.48 cm², cost = ₹ 207.24.

Scoring tip: Say in words that the joining circle is hidden. It shows the examiner why you did not add the two total surface areas.