What is the mathematical relationship between the radius $(r)$ of a cylindrical conductor and its cross-sectional area $(A)$?

$A$ conductivity cell containing $0.001 \ M$ $AgNO_3$ solution develops resistance $6530 \ \Omega$ at $25 \ ^{\circ}C$. Calculate the electrical conductivity of the solution at the same temperature if the cell constant is $0.653 \ cm^{-1}$.

The dissociation constant of acetic acid is $1.75 \times 10^{-5}$ and $\Lambda _{CH_3COOH}^o = 370.6 \times 10^{-4} \, S \, m^2 \, mol^{-1}$. The specific conductance of $0.01 \, M$ acetic acid solution will be:

Which of the following $M$ $KCl$ solutions has the lowest value of equivalent conductance?

What is the conductivity of $0.02 \ M \ KCl$ solution if the cell constant is $1.29 \ cm^{-1}$ and the resistance is $645 \ \Omega$?

Molar conductances of $BaCl_2, H_2SO_4$ and $HCl$ at infinite dilutions are $x_1, x_2$ and $x_3$ respectively. Equivalent conductance of $BaSO_4$ at infinite dilution will be