Multiple choice

Consider a hollow cylinder of inner radius $r$ and thickness of wall $t$ and length $l$. The volume of the above cylinder is given by

  1. $2\pi l t \left ( r^2-l^2 \right )$
  2. $ \displaystyle 2\pi rl t \left( \frac{t}{2r}+1 \right )$
  3. $2\pi l t \left ( r^2+l^2 \right )$
  4. $2\pi rl t\left ( r+t \right )$
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B Correct answer
Explanation

Volume = Outer Cylinder Volume - Inner Cylinder Volume. Outer radius = r+t. Volume = pi * (r+t)^2 * l - pi * r^2 * l = pi * l * ((r+t)^2 - r^2) = pi * l * (r^2 + 2rt + t^2 - r^2) = pi * l * (2rt + t^2) = pi * l * t * (2r + t) = 2 * pi * r * l * t * (1 + t/(2r)).

AI explanation

Using the volume of a hollow cylinder formula V equals pi times the outer radius squared minus the inner radius squared times length, we substitute the outer radius as (r + t). This gives V = pi * ((r + t)^2 - r^2) * l = pi * (r^2 + 2rt + t^2 - r^2) * l = pi * (2rt + t^2) * l. Factoring out 2r from the terms in parentheses gives V = pi * 2r * (t + t^2/2r) * l = 2 * pi * r * l * t * (t/2r + 1).

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