Multiple choice

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is H cm and the diameter of the cylinder is 2 r cm. The volume of the solid is

  1. $\pi r^2\left (H-\dfrac {2r}{3}\right )cm^3$
  2. $\pi r^2\left (H+\dfrac {2r}{9}\right )cm^3$
  3. $\pi r^2\left (H-\dfrac {2r}{9}\right )cm^3$
  4. $\pi r\left (H-\dfrac {2r}{3}\right )cm^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The solid consists of a cylinder of height (H - 2r) and two hemispheres which form a sphere of radius r. Volume = pi * r^2 * (H - 2r) + (4/3) * pi * r^3 = pi * r^2 * (H - 2r + 4r/3) = pi * r^2 * (H - 2r/3).

AI explanation

The solid consists of a cylinder of height (H - 2r) cm and radius r cm, and two hemispheres of radius r cm. Using the volume formulas, the cylinder volume is pi * r^2 * (H - 2r) and the combined volume of the two hemispheres is (4/3) * pi * r^3. Adding these gives pi * r^2 * (H - 2r) + (4/3) * pi * r^3, which simplifies to pi * r^2 * (H - 2r + 4r/3) and results in pi * r^2 * (H - 2r/3).

Keep practicing — related questions