**CBSE Class 9 Maths Surface Areas and Volumes Notes:-**Download PDF Here

The surface area and volume for class 9 notes are given here. In this article, you are going to discuss the complete surface area and volume formulas for different three-dimensional shapes are discussed here with the complete explanation. For any three-dimensional figures, the surface area can be broadly classified into Curved Surface Area(CSA), Lateral Surface Area (LSA), and Total Surface Area (TSA) are given for 3d shapes such as a cube, cuboid, cone, cylinder and so on.

### Cuboid

A cuboid is a three dimensional Shape. The cuboidÂ 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.

### Total Surface Area of a Cuboid

Consider a cuboid whose length is “*l”Â *cm, breadth is *b* cm and height *h* cm.

Area of face ABCD = Area of Face EFGH =(lÃ—b)cm2

Area of face AEHD = Area of face BFGC =(bÃ—h)cm2

Area of face ABFE = Area of face DHGC =(lÃ—h)cm2

Total surface area (TSA) of cuboid = Sum of the areas of all its six faces

=2(lÃ—b)+2(bÃ—h)+2(lÃ—h)

TSA (cuboid)= 2(lb + bh +lh)

### 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(bÃ—h)+2(lÃ—h)

LSA (cuboid) = 2h(l + b)

### Cube

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

### Total Surface Area of a cube

For cube, length = breadth = height

Suppose length of an edge = a

Total surface area(TSA) of the cube =2(aÃ—a+aÃ—a+aÃ—a)

TSA(cube) =2Ã—(3a2)=6a2

### 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(aÃ—a+aÃ—a)=4a2

### Right Circular Cylinder

A right circular cylinder is a closed solid that has two parallel circular bases connected by a curved surfaceÂ 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 can be transformed into a rectangle of length 2Ï€r and height *h* units. Thus,

Curved surface area(CSA) of a cylinder of base radius *r*Â and height *h* =2Ï€Ã—rÃ—h

### Total surface area of a right circular cylinder

Total surface area(TSA)Â of a cylinder of base radius *r* and height *h* = 2Ï€Ã—rÃ—h + area of two circular bases

â‡’ TSA =2Ï€Ã—rÃ—h+2Ã—Ï€r2

â‡’ TSA =2Ï€r(h+r)

### Right Circular Cone

A right circular cone is a circular cone whose axis is perpendicular to its base.

### Relation between slant height and height of a right circular cone

The relationship between slant height(*l*) and height(*h*) of a right circular cone is:

l2=h2+r2Â Â (Using Pythagoras Theorem)

Where *r* is the radius of the base of the cone.

### Curved Surface Area of a Right Circular Cone

Consider a right circular cone with slant length *l*Â and radius *r*.

If a perpendicular cut is made from a point on the circumference of the base to the vertex and the cone is opened up,Â a sector of a circle with radius *l*Â is produced as shown in the figure below:

Label A and B and corresponding b1, b2 …bn at equal intervals, with O as the common vertex. The Curved surface area(CSA) of the cone will be the sum of areas of the small triangles: 12Ã—(b_{1}+b_{2}.……..b_{n})Ã—l

(b1+b2...bn) is also equal to the circumference of base =2Ï€r

CSA of right circular cone =(1/2)Ã—(2Ï€r)Ã—l=Ï€rlÂ Â Â Â Â (On substituting the values)

### Total Surface Area of a Right Circular Cone

Total surface area(TSA) = Curved surface area(CSA) + area of base =Ï€rl+Ï€r2=Ï€r(l+r)

### 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* =4Ã—(Ï€r2)

For a sphere Curved surface area (CSA) = Total Surface area(TSA) = 4Ï€r2

### Volume of a Cuboid

The volume of a cuboid is the product of its dimensions.

Volume of a cuboid = lengthÃ—breadthÃ—height= lbh

Where *l* is the length of the cuboid, *b* is the breadth, and *h* is the height of the cuboid.

### Volume of a Cube

The volume of a cube = baseÂ areaÃ—height.

Since all dimensions are identical, the volume of the cube =a3

Where *a* is the length of the edge of the cube.

### Volume of a Right Circular Cylinder

The volume of a right circular cylinder is equal to base area Ã— its height.

The volume of cylinder =Ï€r2h

Where *r* is the radius of the base of the cylinder and *h* is the height of the cylinder.

### Volume of a Right Circular Cone

The volume of a Right circular cone is 1/3Â times the volume of a cylinder with the same radius and height. In other words, three cones make one cylinder of the same height and base.

The volume of right circular cone =(1/3)Ï€r2h

Where *rÂ *is the radius of the base of the cone and *hÂ *is the height of the cone.

### Volume of a Sphere

The volume of a sphere of radius *r* =(4/3)Ï€r3

### Volume and Capacity

The **volume** of an object is the measure of the space it occupies and the **capacity** of an object is the volume of substance its interior

can accommodate. The unit of measurement of either volume or capacity is cubic unit.