Question

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Answer 1

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:

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

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:

$A^2=\pi^2 r^2(r^2+h^2)$

Dividing by $\pi r^2$

$\displaystyle \frac{A^2}{\pi^2 r^2}=r^2+h^2$

Subtracting $r^2$:

$\displaystyle \frac{A^2}{\pi^2 r^2}-r^2=h^2$

Taking square root:

$\displaystyle h=\sqrt{ \frac{A^2}{\pi^2 r^2}-r^2}$

Substituting the values:

$\displaystyle h=\sqrt{ 251.472-22.5625}$

$\displaystyle h=\sqrt{ 228.909}$

h = 15.13 cm