10th Class Mathematics Mensuration Surface Area of Solids

We are familiar with some of the basic solids like cuboid, cone, cylinder, and sphere. In this chapter we will discuss about how to find the surface area and volume of these figures in our daily life, we come across number of solids made up of combinations of two or more of the basic solids.  

      Surface Area of Solids

We may get the solids which may be combinations of cylinder and cone or cylinder and hemisphere or cone and hemisphere and so on. In such cases we find the surface area of each part separately and add them to get the surface area of entire solid.  

       Cylinder

If 'r' is the radius and 'h' is the height of the cylinder, then

Curved surface area of the cylinder \[=2\pi rh\]

Total surface area of the cylinder = \[27\pi r(r+h)\]  

       Cone

If 'r' be the radius and 'h' be the height of the cone, then

Curved surface area of the cone \[=2\pi rl\]

Total surface area of the cone \[=\pi r(r+l)\]

Where, I is the slant height of the cone and is given by

\[1=\sqrt{{{r}^{2}}+{{h}^{2}}}\]  

       Sphere

If 'r' be the radius of the sphere, then             

Surface area of the sphere \[=4\pi \,{{r}^{2}}\]  

       Hemisphere

If 'r' be the radius of the hemisphere, then

Curved surface area of the hemisphere \[=2\pi \,{{r}^{2}}\]

Total Surface area of the hemisphere \[=3\,\pi \,\,{{r}^{2}}\]