NCERT Class 10 Mathematics Formula CBSE Board Sample Problems Part 10 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Surface Area and Volume

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

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

3Areaa) The area of the plane figure is the surface enclosed by its boundary

b) It 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 Litre
1 1000 L
1 1 L

Surface Area and Volume of Cube and Cuboid

Cube Cuboid

Cube 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 center 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
Surface Area and Volume of Right Circular Cone
TypeMeasurement
Curved or lateral Surface Area of cone
Total surface area of cone
Volume of cone

Surface Area and Volume of Sphere and Hemisphere

Sphere 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 Circle
Area of Circle
The circumference of a circle is .

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, (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,

Surface Area and Volume of Frustum of Cone

Surface Area and Volume of Frustum of Cone

h, = vertical height of the frustum

l = slant height of the frustum

and are radii of the two bases (ends) of the frustum.

Surface Area and Volume of Frustum of Cone
TypeMeasurement
Volume of a frustum of a cone
Slant height of frustum of a cone
Curved surface area of a frustum of a cone
Total surface area of frustum of a cone