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Title: Surface area and volume
Description: Detailed formulas of surface area and volume chapter

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Surface Areas and Volumes
Cuboid
A cuboid is a three-dimensional Shape
...
The total surface area of a cuboid is
equal to the sum of the areas of its six rectangular faces
...

Area of face ABCD = Area of Face EFGH = (l × b) cm2
Area of face AEHD = Area of face BFGC = (b × h) cm2
Area of face ABFE = Area of face DHGC = (l × h) cm2
Total surface area (TSA) of cuboid = Sum of the areas of all its six faces
= 2(l × b) + 2(b × h) + 2(l × 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
...
It is a
three-dimensional shape bounded by six equal squares
...


Total Surface Area of a Cube

For cube, length = breadth = height
Suppose the length of an edge = a
Total surface area(TSA) of the cube = 2(a × a + a × a + a × a)
TSA(cube) = 2 × (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
...


Curved Surface Area of a Right Circular Cylinder
Take a cylinder of base radius r and height h units
...
Thus,

Curved surface area(CSA) of a cylinder of base radius r and
height h = 2π × r × h

Total Surface Area of a Right Circular Cylinder
Total surface area(TSA) of a cylinder of base radius r and
height h = 2π × r × h + area of two circular bases
⇒ TSA = 2π × r × h + 2 × πr2
⇒ TSA = 2πr(h + r)

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


Curved Surface Area of a Right Circular Cone
Consider a right circular cone with slant length l and radius r
...
The Curved surface area(CSA) of the cone will be the sum of the
areas of the small triangles: 1/2 × (b1 + b2
...
bn) is also equal to the circumference of base = 2πr
CSA of right circular cone = (1/2) × (2πr) × l = πrl
(On substituting
the values)

Total Surface Area of a Right Circular Cone
Total surface area(TSA) = Curved surface area(CSA) + area of
base = πrl + πr2 = πr(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”
...


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

Surface Area Formulas
Shapes

Surface Areas

Cuboid

2(lb + bh + hl)

Cube

6a2

Right Circular Cylinder

2πr(r + h)

Right Circular Cone

πr(l + r), ( l2 = h2 + r2 )

Sphere

4 π r2

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


Volume of a Cube
The volume of a cube = base area × height
...


Volume of a Right Circular Cylinder
The volume of a right circular cylinder is equal to base area × its height
...


Volume of a Right Circular Cone
The volume of a Right circular cone is 1/3 times the volume of a cylinder with the
same radius and height
...

The volume of right circular cone = (1/3)πr2h
Where r is the radius of the base of the cone and h is the height of the cone
...


Volume Formulas
Shapes

Volumes

Cuboid

length × breadth × height

Cube

a3

Right Circular Cylinder

πr2h

Right Circular Cone

⅓ πr2h

Sphere

4/3 π 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
...



Title: Surface area and volume
Description: Detailed formulas of surface area and volume chapter