ठोसों के संयोजन का पृष्ठीय क्षेत्रफल: Difference between revisions
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[[File:Combination of solids.jpg|alt=Fig 1 - Surface area of combination of solids|thumb|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 =<math>2\Pi r^2</math> | |||
Curved Surface Area (CSA) of cylinder =<math>2\Pi rh</math> | |||
== 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 <math>h=10 , r=3.5</math> | |||
Total Surface Area (TSA) of wooden article = Curved Surface Area (CSA) of cylinder + 2 X Curved Surface Area (CSA) of hemisphere | |||
<math>=2\Pi rh +2 \times 2\Pi r^2</math> | |||
<math>=2 \times \frac{22}{7} \times 3.5 \times 10 +2 \times 2 \times \frac{22}{7} \times 3.5^2</math> | |||
<math>=220+154 =374 </math> cm<sup>2</sup> | |||
The total surface area of the article is <math>374 </math> cm<sup>2</sup> | |||
[[Category:पृष्ठीय क्षेत्रफल और आयतन]] | [[Category:पृष्ठीय क्षेत्रफल और आयतन]] | ||
[[Category:गणित]][[Category:कक्षा-10]] | [[Category:गणित]][[Category:कक्षा-10]] | ||
Revision as of 09:20, 29 August 2024
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 =
Curved Surface Area (CSA) of cylinder =
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
Total Surface Area (TSA) of wooden article = Curved Surface Area (CSA) of cylinder + 2 X Curved Surface Area (CSA) of hemisphere
cm2
The total surface area of the article is cm2