Surface Areas and Volumes Class 9 Notes Maths Chapter 13

 

CBSE Class 9 Maths Notes Chapter 13 Surface Areas and Volumes

1. Cuboid: A figure which is surrounded by six rectangular surfaces is called cuboid.
The opposite surface of a cuboid is equal and parallel.

A cuboid has 12 edges and 8 corners. Each corner of a cuboid is called the vertex of a cuboid. The line segment joining the opposite vertices is called the diagonal of a cuboid. There are four diagonals in a cuboid.

Volume of cuboid = Length × Breadth × Height = l × b × h
Lateral surface area = 2 (Length + Breadth) × Height = 2 (l + b) × h
Total surface area = 2 (Length × Breadth + Breadth × Height + Height × Length) = 2 (lb + bh + hl)
Total length of cuboid = 4 (l + b + h)

2. Cube: A cuboid, whose length, breadth and height are same is called a cube.
A cube has six surfaces, twelve edges, eight corners and four diagonals.
Volume of cube= (Side)³ = l³
Lateral surface area = 4 × (Side)² = 4l²
Total surface area = 6 × (Side)² = 6l²
Total length of cube = 12l
Diagonal of cube = √3 l

3. Right Circular Cylinder: A right circular cylinder is considered as a solid generated by the revolution of a rectangle about one of its sides.

The volume of a cylinder = πr²h
Curved surface area or lateral surface area = 2πrh
Total surface area = Curved surface + 2 × Base area = 2πrh + 2πr² = 2πr(h + r)

4. Cone: A right circular cone is a solid generated by revolving of a triangle about one of its sides (other than hypotenuse).

Volume of cone = \(\frac { 1 }{ 3 }\) πr²h
Curved surface area or lateral surface area = πrl
Total surface area = Curved surface area + Base area

5. Sphere: A solid which is surrounded by a curved surface and each point of the surface is the same distance from a fixed point. The fixed point is called the centre of the sphere. The line segment joining from the centre of the sphere to any point of the surface is called the radius of the sphere.

6. Hemisphere: A plane passing through the centre of a sphere divides the sphere into two equal parts. Each part is called a hemisphere.

Volume of hemisphere = \(\frac { 2 }{ 3 }\) πr³
The curved surface area of hemisphere = 2πr²
Total surface area of hemisphere = 2πr² + πr² = 3πr²

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