Surface area of a cylinder · 2 marks

Savitri had to make a model of a cylindrical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope (see the figure). What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 25 cm with a 3.5 cm radius? You may take π = 227.

Answer: Chart paper = curved surface area = 2πrh = 2 × 227 × 3.5 × 25 = 550 cm².

Step-by-step solution

Given: Radius r = 3.5 cm; Height (length) h = 25 cm; π = 227
To find: Area of chart paper (curved surface only)

Idea: Only the curved surface is made of chart paper (the ends are lenses/glass), so use CSA = 2πrh. The length of the tube is its height.

Radius r = 3.5 cm; height (length of the tube) h = 25 cm.½ mark
Area of chart paper = curved surface area = 2πrh = 2 × 227 × 3.5 × 25 cm².½ mark
227 × 3.5 = 11, so this is 2 × 11 × 25 = 550 cm².1 mark

Area of chart paper required = 550 cm².

Check: Opened out, the paper is a rectangle 2πr = 22 cm long and 25 cm wide: 22 × 25 = 550 cm² ✓.

r = 3.5 cm, h = 25 cm

Area of chart paper = CSA = 2πrh

= 2 × 227 × 3.5 × 25

∴ Area = 550 cm²

Adding the two circular ends (TSA) when only the curved surface is made of chart paper.
Taking 3.5 cm as the diameter.

MCQ (1 mark)

A cardboard tube of radius 2.1 cm and length 30 cm is to be covered with paper (curved part only). Paper needed is (π = 227)

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(B) 396 cm²
2 × 227 × 2.1 × 30 = 13.2 × 30 = 396 cm².

A roller of radius 35 cm and length 1 m rolls once over a lawn. What area does it press? (π = 227)

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CSA = 2 × 227 × 35 × 100 = 22,000 cm² = 2.2 m².