Ex 11.4 Q1,2,3,4,5,6,7. SAV. NCERT 9CBSE

Surface Areas and Volumes – Class 9 CBSE

Surface Areas and Volumes is an important chapter of Class 9 Mathematics that deals with the study of three-dimensional (3D) solids. In this chapter, we learn how to calculate the outer surface area and the space occupied by different solids. These concepts are widely used in real-life applications such as finding the capacity of containers, cost of painting, polishing, and construction work.


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Three-Dimensional Solids

Three-dimensional solids have length, breadth, and height. Unlike plane figures, they occupy space and have measurable surface area and volume.
Common solids studied are cube, cuboid, cylinder, cone, sphere, and hemisphere.


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Surface Area

Surface area is the total area of the outer surface of a solid.

Curved Surface Area (CSA): Area of the curved portion only.

Total Surface Area (TSA): Area of all faces including curved and flat surfaces.



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Volume

Volume is the amount of space occupied by a solid. It is measured in cubic units. Each solid has a fixed formula to calculate its volume.


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Combination of Solids

Some solids are formed by combining two or more basic solids. While solving such problems:

Add volumes of individual solids

Add only exposed surface areas

Common surfaces are not included



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Applications of Surface Areas and Volumes

These concepts are used in daily life for:

Finding capacity of tanks

Calculating cost of painting or polishing

Determining material required

Solving practical word problems



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Conclusion

The chapter Surface Areas and Volumes helps students understand real-life geometry, improves logical thinking, and builds a strong foundation for higher classes.


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