Multiple choice

An oxygen cylinder is in the form of a right circular cylinder with a cone at one end and a hemisphere at the other end. Their common radius is r and height of cylindrical part is H cm and that of conical part is h cm. Express the volume V in terms of H, h & r

  1. $V=\frac {\pi r^2}{3}(h+H+2r)$
  2. $V=\frac {\pi r^2}{3}(h+2H+2r)$
  3. $V=\frac {\pi r^2}{3}(h+3H+4r)$
  4. $V=\frac {\pi r^2}{3}(h+3H+2r)$
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D Correct answer
Explanation

Total volume = Volume of cylinder + Volume of cone + Volume of hemisphere. V = pi*r^2*H + (1/3)*pi*r^2*h + (2/3)*pi*r^3. Factoring out (pi*r^2)/3 gives (pi*r^2)/3 * (3H + h + 2r).

AI explanation

The total volume V is the sum of the volumes of the cone, the cylinder, and the hemisphere. Using the volume formulas gives V = (1/3)πr^2h + πr^2H + (2/3)πr^3. Factoring out (πr^2)/3 yields V = (πr^2)/3 * (h + 3H + 2r). The result is V = (πr^2)/3(h + 3H + 2r).

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