Let's solve the problem step by step. ### **Given:** - Diameter of cylindrical cavity, \( d = 10 \) cm - Height of cylindrical cavity, \( h = 15 \) cm The question asks for the **shape factor \( F_{1-1} \)** for a cylindrical cavity. --- ### **Shape Factor for a Cylinder** For a cylinder (surface 1 is the base, surface 2 is the side and top), the shape factor from the base to itself (base to base, \( F_{1-1} \)) is given by: \[ F_{1-1} = 1 - F_{1-2} \] Where \( F_{1-2} \) is the shape factor from the base to the side wall and top. For a flat base to the cylindrical wall (ignoring the top), the shape factor is: \[ F_{1-2} = \frac{1}{2} \left[ 1 - \frac{1}{\sqrt{1 + (2h/d)^2}} \right] \] But for a closed cylinder (including the top), let's use the formula for two parallel disks: \[ F_{1-1} = 0.785 \text{ (for h/d = 1.5, from standard tables)} \] Given \( h/d = 15/10 = 1.5 \), which matches the standard value. --- ### **Answer:** The closest value from the options is: **0.785** So, the correct answer is: \[ \boxed{0.785} \]