ठोसों के संयोजन का पृष्ठीय क्षेत्रफल

Fig 1 - Surface area of combination of solids

Let us consider the container shown in Fig. 1. How do we find the surface area of such a solid?This solid is made up of a cylinder with two hemispheres stuck at either end.

Total Surface Area (TSA) of new solid = Curved Surface Area (CSA) of one hemisphere +

Curved Surface Area (CSA) of cylinder + Curved Surface Area (CSA) of other hemisphere

Curved Surface Area (CSA) of hemisphere =$2\Pi r^{2}$

Curved Surface Area (CSA) of cylinder =$2\Pi rh$

Example

1.A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm,

find the total surface area of the article.

Solution:

Here $h=10,r=3.5$

Total Surface Area (TSA) of wooden article = Curved Surface Area (CSA) of cylinder + 2 X Curved Surface Area (CSA) of hemisphere

$=2\Pi rh+2\times 2\Pi r^{2}$

$=2\times {\frac {22}{7}}\times 3.5\times 10+2\times 2\times {\frac {22}{7}}\times 3.5^{2}$

$=220+154=374$ cm²

The total surface area of the article is $374$ cm²