NCERT Class 9 Mathematics Surface Area and Volume Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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Mensuration

It is branch of mathematics which is concerned about the measurement of length, area and Volume of plane and Solid figure

Perimeter

The perimeter of plane figure is defined as the length of the boundary

It units is same as that of length i.e.. m, cm, km

It Units is Same as That of Length
1 Meter10 Decimeter100 centimeter
1 Decimeter10 centimeter100 millimeter
1 Km10 Hectometer100 Decameter
1 Decameter10 meter1000 centimeter

Surface Area or Area

The area of the plane figure is the surface enclosed by its boundary

It unit is square of length unit. i.e..

Surface Area or Area
1 square Meter100 square Decimeter10000 square centimeter
1 square Decimeter100 square centimeter10000 square millimeter
1 Hectare100 square Decameter10000 square meter
1 square myraimeter100 square kilometer square meter

Volume

Surface Area or Area
1mL
1 Litre1000 ml
1000 L
1 L

Surface Area

Surface Area and Volume of Cube and Cuboid

Surface Area and Volume of Cube and 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 cuboids
Length of all 12 edges of the cuboids
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
Surface Area and Volume of Right Circular Cylinder
RadiusThe radius (r) of the circular base is called the radius of the cylinder
HeightThe length of the axis of the cylinder is called the height (h) of the cylinder
Lateral SurfaceThe curved surface joining the two base of a right circular cylinder is called Lateral Surface.
Surface Area and Volume of Right Circular Cylinder
TypeMeasurement
Curved or lateral Surface Area of cylinder
Total surface area of cylinder
Volume of Cylinder

Surface Area and Volume of Right circular cone

Surface Area and Volume of Right Circular Cone
RadiusThe radius (r) of the circular base is called the radius of the cone
HeightThe length of the line segment joining the vertex to the centre of base is called the height (h) of the cone.
Slant HeightThe 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 AreaThe curved surface joining the base and uppermost point of a right circular cone is called Lateral Surface
Type Measurement
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
Surface Area and Volume of Sphere and Hemisphere
SphereA sphere can also be considered as a solid obtained on rotating a circle About its diameter
HemisphereA plane through the centre of the sphere divides the sphere into two equal parts, each of which is called a hemisphere
RadiusThe radius of the circle by which it is formed
Spherical ShellThe difference of two solid concentric spheres is called a spherical shell
Lateral Surface Area for SphereTotal surface area of the sphere
Lateral Surface area of HemisphereIt is the curved surface area leaving the circular base
Surface Area and Volume of Sphere and Hemisphere
TypeMeasurement
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

How the Surface Area and Volume Are Determined
Area of CircleThe circumference of a circle is . This is the definition of (pi) . Divide the circle into many triangular segments. The area of the triangles is times the sum of their bases, (the circumference) , times their height, r.

Surface Area of cylinder
Surface Area of Cylinder
This can be imagined as unwrapping the surface into a rectangle.
Surface area of coneThis 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,

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