The radius of cone shaped funnel is 5 inches
Solution:
To calculate the volume of a cone, we have to multiply the base area, in this case the area of a circle:
[tex]\pi r^2[/tex] by its height and by [tex]\frac{1}{3}[/tex]
[tex]\bold{Volume \ of \ a \ cone \ is \ \frac{1}{3} \times \pi\times r^2\times h}[/tex]
Here, volume = 314; h = 12;
we already know [tex]\bold{\pi=3.14}[/tex]
On substituting the vales we get,
[tex]314=\frac{1}{3}\times 3.14\times r^2\times 12[/tex]
Bringing 3.14 to the L.H.S,
[tex]\frac{314}{3.14}=\frac{1}{3}\times r^2\times12[/tex]
On solving we get,
[tex]100=4\times r^2[/tex]
[tex]\frac{100}{4}=r^2[/tex]
On dividing 100 and 4 we get,
[tex]25=r^2[/tex]
Taking roots on both sides,
[tex]\sqrt25=\sqrt{r^2}[/tex]
[tex]\sqrt{5\times5}=\r[/tex]
[tex]\therefore r=5[/tex]
Hence, radius = 5 inches
