Surface Area of a Half Sphere

sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface laying the same distance r from the center point. The half sphere means, it has half the shape of sphere. The shape of the sphere is shown in below. Let us see how to calculate the surface area of the half the sphere.

sphere and half sphere

 

Formula to find surface area of half sphere:

 

            Surface area of the sphere (SA) = 4 π r2 square units

                                                            r – Radius of the sphere

             Surface area of the half the sphere (SA) = area of the sphere/ 2

                                                                                        = 4 π r2 / 2

                                                                                       = 2 π r2 square units

 

Example Problems to Find Surface Area:

 

  1. The sphere has the radius 5. 7 cm. find the half the surface area of sphere

Solution:

      Given:

                  Radius of sphere (r) = 5.7 cm

      Formula:

      Surface area of the half the sphere (SA) = 2 π r2 square units

                                                                                  = 2 x 3.14 x 5.72

                                                                                  = 204.0372

      Surface area of the half the sphere (SA) = 204.0372 cm2

 

 

2.The sphere has the radius 7.5 cm. find the half the surface area of sphere

Solution:

      Given:

                  Radius of sphere (r) = 7.5 cm

      Formula:

      Surface area of the half the sphere (SA) = 2 π r2 square units

                                                                                  = 2 x 3.14 x 7.52

                                                                                  = 353.25

      Surface area of the half the sphere (SA) = 353.25 cm2 

3.The sphere has the radius 8.3 cm. find the half the surface area of sphere

Solution:

      Given:

                  Radius of sphere (r) = 8.3 cm

      Formula:

      Surface area of the half the sphere (SA) = 2 π r2 square units

                                                                                  = 2 x 3.14 x 8.32

                                                                                 = 432.62

      Surface area of the half the sphere (SA) = 432.62 cm2

 

Surface Area of a Half Sphere - Practice Problems

1.The sphere has the radius 4.4  cm. find the half the surface area of sphere

Answer: Surface area of the half the sphere = 121.58 cm2

2.The sphere has the radius 3.3  cm. find the half the surface area of sphere

Answer: Surface area of the half the sphere = 68.3892 cm2