Question

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is 2R/√3. Also find the maximum volume.

Answer 1

Step-by-step explanation:

So, V is maximum when h = 2R/√3. hence, the height of the cylinder of maximum volume is 2R/√3. Largest volume of the cylinder = π×1/4[4R² - 4R²/3] × 2R/√3 = 4πR³/3√3