Its moment of inertia about the dashed axis through the centre of the cylinder is \( \frac{m a^2 \delta x }{8l}+ \frac{m \delta x }{2l} x^2 = \frac{m(a^2+4x^2) \delta x}{8l}. \) The moment of inertia ...Its moment of inertia about the dashed axis through the centre of the cylinder is \( \frac{m a^2 \delta x }{8l}+ \frac{m \delta x }{2l} x^2 = \frac{m(a^2+4x^2) \delta x}{8l}. \) The moment of inertia of the entire cylinder about the dashed axis is \( 2 \int_{0}^{1} \frac{m(a^2+4x^2) \delta x}{8l} = m(\frac{1}{4}a^2 + \frac{1}{3} l^2)\).