If the effective length of a 32 cm diameter R.C.C. column is 4.40 m, its slenderness ratio, is

slenderness ratio = Le/k
where Le = effective length
k= radius of gyration

k= square root of ( I xx /A)
where I = moment of inertia
A = Area
Ixx= (pie D^4)/64 = (3.14 × 0.32^4)/64 =0.000514
A= (pie D^2)/4 = (3.14 × 0.32^2)/4 =0.080

now, radius of gyration k = square root of (0.000514/0.08)
=0.08

slenderness ratio = Le / k = 4.4÷0.08 = 55

so the answer is option D.

Slenderness Ratio=l/r(min) -------------(1)
Here ,
l=4.4m=440cm
And ,
r(min)=[I/A]^1/2 --------------(2)
Here ,
I=pi*d^4/64
=3.24*(32)^4/64
=51445.76cm^4

Now,
A=pi*d^2/4
=3.14*(32)^2/4
=803.84cm^2
Now putting values in eqn (2)
r(min)=[51445.76cm^4/803.84cm^2]^2
=8cm
Now, putting all the values in eqn (1)
Slenderness Ratio=440cm/8cm
=55.

explain plz?

L/r
R = . 25 d= 8 cm
So, 4.4/.08= 55