Question

Shape factor $F_{11}$ of conical cavity of base diagram 10 cm and height 15cm shown below is

• A. 0.5
• B. 0.67
• C. 0.333
• D. 1

Answer 1

The correct option is B 0.67


$r=\frac{10}{5}=5cm$

$h=15cm$

$f_{2-1}=1\left(Fromgeometry\right)$

Using reciprocity theorem

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

$F_{1-2}=\frac{A_2}{A_1}\times F_{2-1}$

$=\frac{\pi r^2}{\pi r\times \sqrt{r^2+h^2}}$

$=\frac{r}{\sqrt{r^2+h^2}}=\frac{5}{\sqrt{5^2+{15}^2}}$

$=\frac{5}{\sqrt{250}}=0.3162\approx 0.32$

Using summation rule :

$F_{1-1}+F_{1-2}=1$

$F_{1-1}=1-F_{1-2}=1-0.32=0.68$