Multiple choice

It costs Rs.$2200$ to paint the inner curved surface of a cylindrical vessel $10\ m$ deep. If the cost of painting is at the rate of Rs.$20$ per ${m}^{2}$. Find r adius of the base.

  1. $1.75\ m$
  2. $2.75\ m$
  3. $1.25\ m$
  4. $3.75\ m$
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A Correct answer
Explanation

Curved surface area = Total cost / rate = 2200 / 20 = 110 m^2. Formula for CSA = 2 * pi * r * h. 110 = 2 * (22/7) * r * 10. 110 = (440/7) * r. r = 110 * 7 / 440 = 7/4 = 1.75 m.

AI explanation

First, find the inner curved surface area by dividing the total cost by the rate, which gives 2200 divided by 20 to equal 110 square meters. Using the formula for the curved surface area of a cylinder, 2 * pi * r * h, substitute the known values to get 110 = 2 * (22/7) * r * 10. Solving this equation yields 44r = 77, so the radius is 1.75 m.

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