Multiple choice

The inner curved surface area of a hemispherical dome of a building needs to be painted. If the circumference of the base is $17.6m$, find the cost of painting it at the rate of Rs.$5$ per sq.m

  1. Rs.$246.40$
  2. Rs.$24.40$
  3. Rs.$26.40$

  4. None of these
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A Correct answer
Explanation

Circumference of base = 2 * pi * r = 17.6. r = 17.6 / (2 * 3.14) = 2.8 m. Curved surface area of hemisphere = 2 * pi * r^2 = 2 * 3.14 * 2.8 * 2.8 = 49.28 sq.m. Cost = 49.28 * 5 = 246.40.

AI explanation

Using the circumference formula 2 * pi * r = 17.6, the radius of the dome is calculated as 17.6 / (2 * 3.14) = 2.8 m. The inner curved surface area of the hemisphere is 2 * pi * r^2, which equals 2 * 3.14 * 2.8 * 2.8 = 49.28 sq m. Multiplying this area by the painting rate of Rs. 5 per sq m gives a total cost of Rs. 246.40.

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