Multiple choice

The base radius of a cylinder is $1\dfrac {2}{3}$ times its height. The cost of painting its curved surface area at $2\ paise/ cm^{2}$ is Rs. $92.40$. Find the volume of the cylinder.

  1. $80850\ cm^{3}$
  2. $80580\ cm^{3}$
  3. $80508\ cm^{3}$
  4. $800508\ cm^{3}$
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A Correct answer
Explanation

Curved Surface Area (CSA) = Total Cost / Rate = 92.40 / 0.02 = 4620 cm^2. CSA = 2 * pi * r * h. Given r = 5/3 * h. 4620 = 2 * pi * (5/3 * h) * h. Solve for h, then find volume = pi * r^2 * h.

AI explanation

Given the curved surface area cost of Rs. 92.40 at 0.02 Rs per cm^2, the area is 92.40 / 0.02 = 4620 cm^2, which means 2*pi*r*h = 4620. We are given the base radius r = 5/3 * h, so substituting this into the area formula gives 2 * 22/7 * (5/3 * h) * h = 4620. Solving this yields h = 21 and r = 35. The volume is V = pi*r^2*h = 22/7 * 35^2 * 21 = 80850 cm^3.

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