Given:
diameter = 8 in
slant height = 12 in
A diagram of the figure is as follows:
Where:
a = slant height = 12 in
R = radius = diameter/2 = 8/2 = 4 in
h = height
From the figure above we can see that a right triangle is formed, so we use the Pythagorean theorem to find the height of the funnel:
[tex]h^2+R^2=a^2[/tex]
Substitute the values:
[tex]\begin{gathered} h^2+4^2=12^2 \\ h^2+16=144 \end{gathered}[/tex]
And solve for h:
[tex]\begin{gathered} h^2+16-16=144-16 \\ h^2=128 \\ h=\sqrt{128}=11.31 \end{gathered}[/tex]
Answer: the height of the funnel is 11.31 in
