The image above is a spherical segment.
To compute the surface area of a spherical segment requires two essential parameters which are the radius of the sphere (R) and the height (h).
The formula for calculating the surface area of the spherical segment:
A = 2πRh
Where;
A = Surface area of the spherical segment
R = Radius of the sphere
h = Height of the spherical segment
Let’s solve an example;
Find the surface area of a spherical segment when the radius of the sphere is 12 cm and the height is 16 cm.
This implies that;
R = Radius of the sphere = 12 cm
h = Height of the spherical segment = 16 cm
A = 2πRh
A = 2π (12 x 16)
A = 2π (192)
A = 6.28 (192)
A = 1206.37
Therefore, the surface area of the spherical segment is 1206.37 cm2.
Calculating the Radius of the Sphere using the Surface Area of the Spherical Segment and the Height.
R = A / 2πh
Where;
R = Radius of the sphere
A = Surface area of the spherical segment
h = Height of the spherical segment
Let’s solve an example;
Find the radius of a sphere with a surface area of 300 cm2 and a height of 12 cm.
This implies that;
A = Surface area of the spherical segment = 300 cm2
h = Height of the spherical segment = 12 cm
R = A / 2πh
R = 300 / 2 x π x 12
R = 300 / 75.41
R = 3.978
Therefore, the radius of the sphere is 3.978 cm.