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  Surface Areas & Volumes - Class X
Formulae, Relations, Theorems etc.
Surface Areas and Volumes
Surface Area - It is the sum of areas of all visible (exposed) surfaces of a solid.

Volume - It is the three dimentional space occupied by a solid, liquid or gas.

1.Cuboid - It is a solid figure bonded by 6 faces each of which is a rectangle, opposite rectangles being equal in length and breadth

Surface Area of Cuboid or Rectangular Prism = 2(lb+bh+lh) where l is length, b is breadth or width, h is height
lateral Surface Area of Cuboid or Rectangular Prism = 2h(l+b)

Volume of Cuboid or Rectangular Prism = length×breadth×height

2.Cube - It is a solid figure bonded by 6 faces each of which is a square

Surface Area of Cube = 6side^2

Volume of Cube = side^3

3. Cylinder- collection of point at a constant distance from a given line

lateral Surface Area of Cylinder = 2(Pi) r × h
Whole Surface Area of Cylinder = 2(Pi) × h+2 (Pi) r^2,  
where r is radius and h is height of cylinder

4. Cone - It is the solid figure bounded by a plane base and the surface (called the lateral surface) formed by the locus of all straight line segments joining the vertex to the boundary of the base.

lateral Surface Area of Cone = (Pi) × r × l
Whole Surface Area of Cone = (Pi) × r × l + (Pi) r^2
where r is radius and l is slant height of cone 

5. Sphere -a sphere is the locus of all points in three-dimensional space which are at constant distance  from a fixed point of that space, where constant distance is radius

Surface Area of sphere = 4 (Pi) radius^2
Volume of Sphere =   [4 (Pi) radius^3]/3

6. Hemisphere - half of the sphere (a sphere cut by a plane passing through the centre)
lateral Surface Area of hemisphere = 2 (Pi) radius^2
Whole Surface Area of hemisphere = 3 (Pi) radius^2
Volume of Hemisphere =  [2 (Pi) radius^3]/3

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