Multiple choice

The difference between the outer and the inner curved surface areas of an open cylinder is $88:cm^{2}$. If its length is $14$ cm and volume of the material in it is $176:cm^{3}$, find the inner diameter of the cylinder.

  1. $3$ cm
  2. $4 $ cm
  3. $2 $ cm
  4. $1 $ cm
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A Correct answer
Explanation

Let R be outer radius, r be inner radius, h=14. Difference in CSA = 2*pi*h*(R-r) = 88. 2*(22/7)14(R-r) = 88. 88*(R-r) = 88, so R-r = 1. Volume = pi*h*(R^2-r^2) = 176. (22/7)14(R-r)(R+r) = 176. 44*1*(R+r) = 176, so R+r = 4. Solving R-r=1 and R+r=4 gives 2R=5, 2r=3. Inner diameter = 2r = 3.

AI explanation

The difference between the outer and inner curved surface areas is given by 2 * pi * h * (R - r) = 88, so substituting the known height of 14 gives R - r = 1. Using the volume of the material formula 176 = pi * h * (R^2 - r^2), we factor the difference of squares to get 176 = (22/7) * 14 * 1 * (R + r), which means R + r = 4. Solving these equations gives R = 2.5 cm and r = 1.5 cm, so the required inner diameter is 3 cm.

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