Maths · Mensuration · chapter 12 of 14

Class 10 Maths Chapter 12: Surface Areas and Volumes case study question with answers

One case-based question of the kind the board asks in Section E: a passage and a figure, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.

Case study · 4 marks

A gram panchayat in Nashik builds an overhead water tank. The tank is a cylinder of radius 7 m and height 10 m, closed at the top by a hemispherical dome of the same radius, as in the figure. The tank stands on a raised platform, so its flat base is not painted. Before the monsoon, the outer surface of the walls and the dome is to be painted with waterproof paint. Take π = 22/7.

Part 1 · 1 mark

The curved surface area of the cylindrical wall is

(a) 220 m²(b) 440 m²(c) 1540 m²(d) 748 m²

Show answer

Answer: (b) 440 m²

2πrh = 2 × (22/7) × 7 × 10 = 440 m².

Part 2 · 1 mark

The curved surface area of the dome is

(a) 154 m²(b) 462 m²(c) 308 m²(d) 616 m²

Show answer

Answer: (c) 308 m²

2πr² = 2 × (22/7) × 49 = 308 m². 616 m² is a full sphere.

Part 3 · 2 marks

Find the cost of painting the walls and the dome at ₹25 per m².

Answer and marking scheme

Area = 440 + 308 = 748 m² (the joined circle is inside, the base is not painted). Cost = 748 × 25 = ₹18700.

adds the two curved surfaces only: 748 m² (1)
₹18700 (1)

If the dome were replaced by a conical roof of the same radius and slant height 25 m, find the cost of painting the walls and roof at ₹25 per m².

Answer and marking scheme

Roof = πrl = (22/7)(7)(25) = 550 m². Area = 440 + 550 = 990 m². Cost = 990 × 25 = ₹24750.

roof 550 m² and total 990 m² (1)
₹24750 (1)

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