Surface are of a lightbulb

Question

I have this picture:

How could I calculate the area of a "thing" in red square? It is a circle.

Answer 1

Assume the part in red is a spherical cap of radius $r$. Viewed from the center of the sphere, the cap is forming a cone with half-angle $\theta$. We know:

• the base of the cap is a circle with radius $a = r \sin\theta = \frac{127}{2}{\bf mm}$
• the thickness of the cap is $h = r(1-\cos\theta) = 185-150 = 35 {\bf mm}$

This leads to $$(r - h)^2 = (r\cos\theta)^2 = r^2 - a^2\quad\implies\quad r = \frac{h^2+a^2}{2h} = \frac{21029}{280}{\bf mm}$$ and the surface area of the spherical cap is

$$\text{Area} = 2\pi r^2(1-\cos\theta) = 2\pi rh = \pi (h^2+a^2) = \frac{21029\pi}{4}{\bf mm}^2$$

Answer 2

Assuming you are talking about the surface area of the spherical cross section, can you simply use the spherical cap area formulae- Area = 2* pi * r * h ? r = 127/2 mm and h = 35 mm