Mensuration
Telangana Board · Class 10 · Mathematics
Summary of Mensuration for Telangana Board Class 10 Mathematics. Key concepts, important points, and chapter overview.
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Overview
Mensuration deals with measuring the surface area and volume of solid shapes. For Class 10, the main focus is on cuboid, cube, right prism, cylinder, pyramid, cone, sphere, hemisphere, and combinations of these solids. Surface area is used for painting, whitewashing, and covering objects with canvas
Key Concepts
A cuboid has length l
A cuboid has length l, breadth b, and height h. Its formulas are LSA=2h(l+b), TSA=2(lb+bh+hl), and V=lbh.
A cube has side
A cube has side a. Its formulas are LSA=4a^2, TSA=6a^2, and V=a^3.
A regular circular cylinder has radius
A regular circular cylinder has radius r and height h. Its formulas are CSA=2πrh, TSA=2πr(r+h), and V=πr^2h.
A right circular cone has radius
A right circular cone has radius r, height h, and slant height l. Its formulas are CSA=πrl, TSA=πr(l+r), and V=(1/3)πr^2h. The slant height is l=√(r^2
For a sphere of radius r
For a sphere of radius r, CSA=TSA=4πr^2 and V=(4/3)πr^3. For a hemisphere of radius r, CSA=2πr^2, TSA=3πr^2, and V=(2/3)πr^3.
Learning Objectives
- Recall formulas for surface area and volume of common solid shapes
- Find curved surface area and total surface area of standard solids
- Solve problems on combined solids such as cone with hemisphere or cylinder with hemispheres
- Understand when to use surface area and when to use volume
- Apply the idea that volume remains the same during melting and recasting
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