Multiple choice

A hemispherical dome with a radius of 6 metres is to be painted, including the flat circular base, at a rate of Rs. 14 per square metre. What is the total cost of painting the dome?

  1. Rs. 3,376

  2. Rs. 4,376

  3. Rs. 4,752

  4. Rs. 5,700
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The surface area of a hemisphere (including the base) is 3 * pi * r^2. With r=6, area = 3 * 3.14159 * 36 = 339.29 square meters. Total cost = 339.29 * 14 = 4750.06. Using pi = 22/7, area = 3 * (22/7) * 36 = 2376/7. Cost = (2376/7) * 14 = 4752.

AI explanation

The total surface area to be painted is the sum of the curved surface area of the hemisphere, 2πr^2, and the flat circular base area, πr^2, making the formula 3πr^2. Substituting the radius of 6 meters gives a total area of 3 * (22/7) * 6 * 6, which equals 339 3/7 square meters. Multiplying this area by the painting rate of Rs. 14 per square meter results in a total cost of approximately Rs. 4,752.

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