Question

Consider a 15cm diameter sphere placed within a cubical enclosure with a side length of 15cm. The view factory from any one of the square-cube surface to the sphere is

• A. 0.52
• B. 0.09
• C. 0.26
• D. 0.13

Answer 1

The correct option is B 0.09


1 - Outer surface of sphere
2 - Inside surface of all sides of cube

$A_1{F_1}_{-2}=A_2{F}_{2-1}$

$4\pi r^2\times F_{1-2}=6\times a^2{F}_{2-1}$

$4\pi \times \frac{{0.15}^2}{4}=6\times {0.15}^2\times F_{2-1}(\therefore F_{1-2}=1)$

$F_{2-1}=\frac{\pi }{6}\text{(View factor from all 6 sides of cube to the sphere)}$

Vew factor from any one surface to sphere
$=\frac{F_{2-1}}{6}=\frac{\frac{\pi }{6}}{6}=\frac{\pi }{36}\approx 0.09$