Surface Areas & Volumes - Class X |

Formulae, Relations, Theorems etc. |

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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

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

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

Whole Surface Area of Cone = (Pi) × r × l + (Pi) r^2

where r is radius and l is slant height of cone

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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

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

Whole Surface Area of hemisphere = 3 (Pi) radius^2

Volume of Hemisphere = [2 (Pi) radius^3]/3