Question

formula of mensuration

A Area
a side
Perimeter of Square:
P = 4 × a

P Perimeter
a side
Perimeter of the Rectangle:
P= 2 × ( L+B)

Where,

P Perimeter
L Length
B Breadth
Area of the rectangle:
A= L× B

A Area
L Length
B Breadth
Surface area of a cube:
S = 6 × A2

Where,

S The surface area of a cube
A Length of the side of a cube
Surface Area of a Cuboid:
S =2 × (LB + BH + HL)

Where,

S Surface Area of Cuboid
L Length of Cuboid
B Breadth of Cuboid
H Height of Cuboid
Surface Area of a Cylinder:
S= 2 × π × R × (R+H)

Where,

S Surface Area of Cylinder
R The radius of Circular Base
H Height of Cylinder
Surface Area of a Sphere:
S =4 × π × R2

Where,

S Surface Area of Sphere
R Radius of Sphere
Surface Area of a Right circular cone:
S = π × r(l+r)

Where,

S Surface Area of Cone
R The radius of Circular Base
L Slant Height of Cone


Volume of a cube:
V = A3

Where,

V Volume of cube
A side of cube
Volume of Cuboid:
V = L × B × H

V Volume of Cuboid
L Length of Cuboid
B Breadth of Cuboid
H Height of Cuboid
Volume of a Cylinder:
V= π × R2 × H

Where,

V Volume of Cylinder
R The radius of Circular Base
H Height of Cylinder
Volume of a Right circular cone:
V = ( π × R2 × H ) ÷ 3

Where,

V Volume of Cone
R The radius of Circular Base
H Height of Cone
Volume of a Sphere:
V =
4
3
× π × R3

Where,

V Volume of Sphere
R Radius of Sphere
Volume of a Right circular cone:
V =
1
3
× π × R2 × H

Where,

V Volume of Cone
R The radius of Circular Base
H Height of Cone
Solved Examples
Q.1: Find out the height of a cylinder with a circular base of radius 70 cm and volume 154000 cubic cm.

Solution: A given here,

r= 70 cm

V= 154000 cubic cm

Since formula is,

V = π × R2 × H

i.e. h =
V
π
×
R
²
=
154000
15400
= 10 cm

Therefore, height of the cylinder will be 10 ​

Answer 1

Answer:

ANSWER:

Perimeter of square = 4 (Side of the square) = 4 (60 m) = 240 m

Perimeter of rectangle = 2 (Length + Breadth)

= 2 (80 m + Breadth)

= 160 m + 2 × Breadth

It is given that the perimeter of the square and the rectangle are the same.

160 m + 2 × Breadth = 240 m

Breadth of the rectangle = = 40 m

Area of square = (Side)2 = (60 m)2 = 3600 m2

Area of rectangle = Length × Breadth = (80 × 40) m2 = 3200 m2

Thus, the area of the square field is larger than the area of the rectangular field.