OP Malhotra Notes on Surface Area and Volume of 3D Solids (Cuboid and Cube) Class-9 S.Chand ICSE Maths 2026-27. We Provide Step by Step Notes on Cube, Cuboid, Area of cross-section with Chapter Test of S Chand OP Malhotra Maths. Visit official Website CISCE  for detail information about ICSE Board Class-9.

OP Malhotra Notes on Surface Area and Volume of 3D Solids Class-9 S.Chand ICSE Maths 2026-27

Cuboid :

A cuboid is a three dimensional Shape. The cuboid is made from six rectangular faces, which are placed at right angles. The total surface area of a cuboid is equal to the sum of the areas of its six rectangular faces.

Lateral Surface Area of a Cuboid :

Lateral surface area (LSA) is the area of all the sides apart from the top and bottom faces.
The lateral surface area of the cuboid
= Area of face AEHD + Area of face BFGC + Area of face ABFE + Area of face DHGC
$=2(b\times h)+2(l\times h)$
LSA (cuboid) = 2h(l + b)

Volume of a Cuboid :

The volume of a cuboid is the product of its dimensions.
Volume of a cuboid = length × breadth × height lbh
Where l is the length of the cuboid, b is the breadth, and h is the height of the cuboid.

Cube :

A cuboid whose length, breadth and height are all equal, is called a cube. It is a three-dimensional shape bounded by six equal squares. It has 12 edges and 8 vertices.

Lateral Surface area of a cube :

Lateral surface area (LSA) is the area of all the sides apart from the top and bottom faces.
>Lateral surface area of cube = $2(a\times a+a\times a)=4{\mathrm{a²}}^{}$

Volume of a Cube :

The volume of a cube = base × area × height
Since all dimensions are identical, the volume of the cube $={\mathrm{a³}}^{}$
Where a is the length of the edge of the cube.

Practice Questions on Cube and Cuboid :- Exercise-18(a)

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Right Circular Cylinder :

A right circular cylinder is a closed solid that has two parallel circular bases connected by a curved surface in which the two bases are exactly over each other and the axis is at right angles to the base.

The curved Surface area of a right circular cylinder :

Take a cylinder of base radius r and height h units. The curved surface of this cylinder, if opened along the diameter (d = 2r) of the circular base will be transformed into a rectangle of length $2\pi r$ and height h units.

Sphere :

A sphere is a closed three-dimensional solid figure, where all the points on the surface of the sphere are equidistant from the common fixed point called “centre”. The equidistant is called the “radius”.

Surface area of a Sphere :

The surface area of a sphere of radius r = 4 times the area of a circle of radius r = 4(πr²)
For a sphere Curved surface area (CSA) = Total Surface area(TSA) = 4πr²

Cross-section

A cross-section is the exposed 2D surface or face obtained by making a straight cut through a 3D solid object.

Uniform Cross-section

A solid has a uniform cross-section if every slice made parallel to its base results in an identical shape and size. Cubes, cuboids, cylinders, and prisms are standard solids with a uniform cross-section.

Practice Questions on Area of Cross-section :- Exercise-18(b)

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In this chapter, we study all the topics on Surface Area and Volume of 3D Solids like Cube, Cuboid, Area of cross-section and do some practice questions also. Here we solve extra practice questions on this chapter for better understanding.

For extra practice questions on Surface Area and Volume of 3D Solids :- Chapter Test

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— : End of Surface Area and Volume of 3D Solids OP Malhotra S Chand Solutions :–

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