गोले का पृष्ठीय क्षेत्रफल

The surface area of a sphere is defined as the region covered by its outer surface in three-dimensional space.  A Sphere is a three dimensional figure (solid figure), which is made up of all points in the space, which lie at a constant distance called the radius, from a fixed point called the centre of the sphere.Figure shows a sphere of radius $r$.

The formula of total surface area of a sphere is given by:

Surface area of a sphere = $4\pi r^{2}$

The curved surface area of a hemisphere is half the surface area of the sphere, which

is given by

Curved Surface Area of a Hemisphere = $2\pi r^{2}$

here $r$ is the radius of the sphere of which the hemisphere is a part.

Now taking the two faces of a hemisphere, its surface area is given by

Total Surface Area of a Hemisphere = $2\pi r^{2}+\pi r^{2}=3\pi r^{2}$

Examples

!. Find (i) the curved surface area and (ii) the total surface area of a hemisphere of radius $21$ cm.

Solution:

The curved surface area of a hemisphere of radius $21$ cm would be

= $2\pi r^{2}$ = $2\times {\frac {22}{7}}\times 21\times 21=2772$ cm²

the total surface area of the hemisphere would be

$3\pi r^{2}=3\times {\frac {22}{7}}\times 21\times 21=4158$3 cm²