Question

The maximum volume of a right circular cylinder if the sum of its radius and height is 6 m is ______.

Options

• 64 πm³

• 16 πm³

• 32 πm³

• 4 πm³

Answer 1

The maximum volume of a right circular cylinder if the sum of its radius and height is 6 m is 32 πm³. 

Explanation:

In right circular cylinder r + h = 6

By AM ≥ GM

`("r"/2 + "r"/2 + "h")/3 >= root(3)("r"/2 xx "r"/2 xx "h")`

`=> 6/3 >= (("r"^2"h")/4)^(1/3)`

`=> (2)^3 >= ("r"^2"h")/4`

∴ r²h ≤ 32

∴ Maximum value of r²h = 32

Volume of cylinder = πr²h

∴ Maximum volume = π × 32 = 32π m³