Answer:
h = 15.13 cm
Step-by-step explanation:
Lateral Surface Area of a Cone
Given a right circular cone of base radius r and height h, the lateral surface area is given by:
[tex]A=\pi r\sqrt{r^2+h^2}[/tex]
We are given the lateral area of a funnel as A=236.64 square cm and the radius is r=4.75 cm. It's required to find the height of the cone. It can be calculated by solving for h.
Squaring:
[tex]A^2=\pi^2 r^2(r^2+h^2)[/tex]
Dividing by [tex]\pi r^2[/tex]
[tex]\displaystyle \frac{A^2}{\pi^2 r^2}=r^2+h^2[/tex]
Subtracting [tex]r^2[/tex]:
[tex]\displaystyle \frac{A^2}{\pi^2 r^2}-r^2=h^2[/tex]
Taking square root:
[tex]\displaystyle h=\sqrt{ \frac{A^2}{\pi^2 r^2}-r^2}[/tex]
Substituting the values:
[tex]\displaystyle h=\sqrt{ 251.472-22.5625}[/tex]
[tex]\displaystyle h=\sqrt{ 228.909}[/tex]
h = 15.13 cm
