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Updated on 02nd March, 2023 , 3 min read
Mensuration is the branch of mathematics that deals with measuring various geometric figures and shapes. It entails calculating the areas, volumes, and other properties of shapes. Geometry covers various Mensuration formulas that are useful for the exam point. To excel in this topic, you must be familiar with the formulas and concepts used to solve the questions.
2D Shapes- A two-dimensional shape in geometry is a flat plane figure or a shape with only two dimensions, namely length and width. Two-dimensional or 2-D shapes have no thickness and can only be measured on two sides. Only the area and perimeter of two-dimensional shapes can be computed.
3D Shapes- A three-dimensional shape is one with three dimensions: length, width, and thickness. Volume, Curved Surface Area, and Total Surface Area of 3D shapes are calculated.
Terms |
Abbreviation |
Unit |
Definition |
Area |
A |
m2 or cm2 |
The surface covered by the closed shape is known as Area. |
Perimeter |
P |
m or cm |
The measure of the continuous lines along the boundary of a given figure is known as the Perimeter. |
Volume |
V |
m3 or cm3 |
The capacity of a 3D shaped space is known as its Volume. |
Curved Surface Area |
CSA |
m2 or cm2 |
If there is a curved surface, then the total area of that shape is known as its Curved Surface Area. |
Lateral Surface Area |
LSA |
m2 or cm2 |
The total area of all the lateral surfaces a figure surrounds is known as the Lateral Surface Area. |
Total Surface Area |
TSA |
m2 or cm2 |
If there are several surfaces, then the sum of all the areas of all these surfaces is known as the Total Surface Area. |
Square Unit |
- |
m2 or cm2 |
The area covered by a square of side one unit is known as a square unit. |
Cube Unit |
- |
m3 or cm3 |
The volume occupied by a cube having a side of one unit is known as a cube unit. |
A = a2 |
Where,
A = Area
a = Side of the Square
P = 4a |
Where,
P = Perimeter of Square
a = Side of the Square
P = 2 * (L + B) |
Where,
P = Perimeter of Rectangle
L = Length of Rectangle
B = Breadth of Rectangle
A = L * B |
Where,
A = Area of Rectangle
L = Length of Rectangle
B = Breadth of Rectangle
S = 6 * A2 |
Where,
S = Surface Area of Cube
A = Length of Side of Cube
S = 2 * (LB + BH + LH) |
Where,
S = Surface Area of Cuboid
L = Length of Cuboid
B = Breadth of Cuboid
H = Height of Cuboid
S = 2 * π * R * (R + H) |
Where,
S = Surface Area of Cylinder
R = Radius of Circular Base
H = Height of Cylinder
S = 4 * π * R2 |
Where,
S = Surface Area of Cylinder
R = Radius of Circular Base
H = Height of Cylinder
S = π * R * (L + R) |
Where,
S = Surface Area of Cone
R = Radius of Circular Base
L = Slant Height of Cone
V = a3 |
Where,
V = Volume of Cube
a = Side of Cube
V = L * B * H |
Where,
V = Volume of Cuboid
L = Length of Cuboid
B = Breadth of Cuboid
H = Height of Cuboid
V = π * R2 * H |
Where,
V = Volume of Cylinder
R = Radius of Circular Base
H = Height of Cylinder
V = 1/3 * π * R2 * H |
Where,
V = Volume of Cone
R = Radius of Circular Base
H = Height of Cone
V = 4/3 * π * R3 |
Where,
V = Volume of Sphere
R = Radius of Sphere
V = 1/3 * π * R2 * H |
Where,
V = Volume of Cone
R = Radius of Circular Base
H = Height of Cone
Solution: A given here,
R = 70 cm
V= 154000 cubic cm
Since formula is,
V = π * R2 * H
i.e. H =V * π * R²
=15400015400
= 10 cm
Therefore, height of the cylinder will be 10 cm.
Solution: Let ‘a' cm is added in radius and height
π (10+a)² 4 = π (10)² (4 +a)
(10+a)² 4 = 10² (4 +a)
⇒ a = 5 cm