Surface Areas and Volumes
Madhya Pradesh Board · Class 10 · Mathematics
Summary of Surface Areas and Volumes for Madhya Pradesh Board Class 10 Mathematics. Key concepts, important points, and chapter overview.
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Basic solids familiar from Class IX are cuboid, cone, cylinder, and sphere. Many real objects are combinations of these solids. Surface area and volume of such objects are found by breaking them into simpler parts and applying the correct formula to each part. TSA means Total Surface Area and CSA me
Key Concepts
The curved surface area of
The curved surface area of a hemisphere is half of the surface area of a sphere, so it is 2πr².
When solids are joined
When solids are joined, only the exposed parts are counted. The joined flat faces are not included in total surface area.
For a toy formed by
For a toy formed by a cone and a hemisphere joined at their flat faces, total surface area = CSA of hemisphere + CSA of cone.
For a cube with a hemisphere
For a cube with a hemisphere fixed on top, the surface area of the block = TSA of cube – base area of hemisphere + CSA of hemisphere.
A cone mounted on a cylinder
A cone mounted on a cylinder may have a ring-shaped part of the cone base exposed when the cone base is larger than the cylinder base.
Learning Objectives
- Identify common solids formed by combining basic solids
- Find surface area of combined solids by excluding hidden or joined parts
- Apply formulas for curved surface area and total surface area of hemisphere, cone, cylinder, cube, and cuboid
- Calculate surface areas of objects such as tops, blocks, rockets, and bird-baths
- Calculate volumes of combined solids such as sheds, glasses, and toys
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