NCERT Class 9 Maths Formula CBSE Board Sample Problems Part 12 (For CBSE, ICSE, IAS, NET, NRA 2022)

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12. Surface Area and Volume

Surface Area and Volume
S. noTermDescription
1MensurationIt is branch of mathematics which is concerned about the measurement of length, area, and Volume of plane and Solid figure
2Perimeter(a) The perimeter of plane figure is defined as the length of the boundary

(b) Its units are same as that of length i.e.. . , m, cm, km

3Area(a) The area of the plane figure is the surface enclosed by its boundary

(b) Its unit is square of length unit. i.e.. . ,

4VolumeVolume is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder, or pyramid. Its units are always “cubic,” that is, the number of little element cubes that fit inside the figure.

Volume Unit Conversion

Volume Unit Conversion
1 1 mL1000
1 Litre1000 mI1000
1 1000 L
1 1000 1 L

Surface Area and Volume of Cube and Cuboid

Cube and Cuboid

Cube

Cube and Cuboid

Cuboid

Surface Area and Volume of Cube and Cuboid
TypeMeasurement
Surface Area of Cuboid of Length L, Breadth B and Height H
Lateral surface area of the cuboids
Diagonal of the cuboids
Volume of a cuboidsLBH
Length of all 12 edges of the cuboids4 (L + B + H) .
Surface Area of Cube of side L
Lateral surface area of the cube
Diagonal of the cube
Volume of a cube

Surface Area and Volume of Right Circular Cylinder

Surface Area and Volume of Right Circular Cylinder

Radius

The radius (r) of the circular base is called the radius of the cylinder

Height

The length of the axis of the cylinder is called the height (h) of the cylinder

Lateral Surface

The curved surface joining the two base of a right circular cylinder is called Lateral Surface.

The Curved Surface Joining the Two Base of a Right Circular Cylinder is Called Lateral Surface
TypeMeasurement
Curved or lateral Surface Area of cylinder
Total surface area of cylinder
Volume of Cylinder

Surface Area and Volume of Right Circular Cone

Radius

The radius (r) of the circular base is called the radius of the cone

Height

The length of the line segment joining the vertex to the center of base is called the height (h) of the cone.

Slant Height

The length of the segment joining the vertex to any point on the circular edge of the base is called the slant height (L) of the cone.

Lateral surface Area

The curved surface joining the base a′ uppermost point of a right circular cone is called Lateral Surface

Lateral Surface Area
TypeMeasurement
Curved or lateral Surface Area of cone
Total surface area of cone
Volume of Cone

Surface Area and Volume of Sphere and Hemisphere

Surface Area and Volume of Sphere and Hemisphere

Sphere

A sphere can also be considered as a solid obtained on rotating a circle about its diameter

Hemisphere

A plane through the centre of the sphere divides the sphere into two equal parts, each of which is called a hemisphere

Radius

The radius of the circle by which it is formed

Spherical Shell

The difference of two solid concentric spheres is called a spherical shell

Lateral Surface Area for Sphere

Total surface area of the sphere

Lateral Surface area of Hemisphere

It is the curved surface area leaving the circular base

Lateral Surface Area of Hemisphere
TypesMeasurement
Surface area of Sphere
Volume of Sphere
Curved Surface area of hemisphere
Total Surface area of hemisphere
Volume of hemisphere
Volume of the spherical shell whose outer and inner radii and ‘R’ and ‘r’ respectively

How the Surface Area and Volume Are Determined

Area of Circle

The circumference of a circle is 2 nr.

This is the definition of n (pi) . Divide the circle into many triangular segments. The area of the triangles is times the sum of their bases, 2 nr (the circumference) , times their height, r.

Surface Area of cylinder

This can be imagined as unwrapping the surface into a rectangle.

Surface Area of Cylinder
Surface Area of Cylinder

Surface area of cone

This can be achieved by divide the surface of the cone into its triangles, or the surface of the cone into many thin triangles. The area of the triangles is times the sum of their bases, p, times their height,