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 cm ^{2}.**

**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 cm^{2} and a height of 12 cm.

This implies that;

A = Surface area of the spherical segment = 300 cm^{2}

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.**