This document contains formulas and concepts related to mensuration and geometry. It defines formulas for calculating the area and perimeter of rectangles, squares, parallelograms, triangles, right triangles, isosceles right triangles, equilateral triangles, trapezoids, rhombuses, and quadrilateral shapes. It also provides formulas for calculating properties of circles, spheres, hemispheres, cylinders, cones, and other 3D shapes. Several example problems are included for calculating volume, surface area, and other metrics based on the provided dimensions.

2. Topic/Course
Sub-Topic (Example: name of college)
VIT

3. Mensuration

4. Rectangle :
 Area = lb
 Perimeter = 2(l+b)
Square :
 Area = a×a
 Perimeter = 4a
Parallelogram:
 Area = l × h
 Perimeter = 2(l+b)
Mensuration
Triangle :
Area =b×h/2 or √s(s-a)(s-b)(s-c)…………….where
s=a+b+c/2
Right angle Triangle :
 Area =1/2(bh)
 Perimeter = b+h+d
Isosceles right angle triangle :
 Area = ½. a2
 Perimeter = 2a+d………where d=a√2
IMPORTANT FORMULAE:

5. Equilateral Triangle :
 Area = √3. a2/4 or ½(ah)….where h = √3/2
 Perimeter = 3a
Trapezium :
 Area = 1/2h(a+b)
 Perimeter = Sum of all sides
Rhombus :
 Area = d1 × d2/2
 Perimeter = 4l
Mensuration

6. Quadrilateral:
Area =1/2 × Diagonal × (Sum of offsets)
Circle :
 Area = πr^2 or πd^2/4
 Circumference = 2πr or πd
 Area of sector of a circle = (θπr^2 )/360
Sphere:
 Volume: V = 4/3 πr3
 Surface Area: S = 4πr2
Mensuration

7. Hemisphere :
 Volume = 2/3 π r3
 Curved surface area(CSA) = 2 π r2
 Total surface area = TSA = 3 π r2
Right Circular Cylinder :
 Volume of Cylinder = π r2 h
 Lateral Surface Area (LSA or CSA) = 2π r h
 Total Surface Area = TSA = 2 π r (r + h)
 Volume of hollow cylinder = π r h(R2 – r2)
Right Circular cone :
 Volume = 1/3 π r2h
 Curved surface area: CSA= π r l
 Total surface area = TSA = πr(r + l )
Mensuration

8. Some other Formula :
 Area of Pathway running across the middle of a rectangle =
w(l+b-w)
 Perimeter of Pathway around a rectangle field = 2(l+b+4w)
 Area of Pathway around a rectangle field =2w(l+b+2w)
 Perimeter of Pathway inside a rectangle field =2(l+b-4w)
 Area of Pathway inside a rectangle field =2w(l+b-2w)
 Area of four walls = 2h(l+b)
Mensuration

9. If area of square field is 6.76 hectare, then its length is __________ m.
A)
B)
C)
D)
260
275
290
315
Question 1

10. Let the diameter be 14 cm and height be 6 cm. Find the volume of cylinder
and cone. (in cm3)
A)
B)
C)
D)
800,400
924,308
1024,484
None of these
Question 2

11. How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?
A)
B)
C)
D)
10
50
100
1000
Question 3

12. The area of a rectangular ground is 12500 m2. If its length is 125 m, then its
perimeter is(in m)
A)
B)
C)
D)
450
500
575
625
Question 4

13. In a triangle PQR, PQ = QR = 10 cm, PR = 12 cm. QS is drawn
perpendicular to PR where s is on the line PR. Find the length of QS.(in cm)
A)
B)
C)
D)
8
10
12.5
None of these
Question 5

14. A triangle is made from a rope. The sides of triangle are 21 cm, 15 cm and
32 cm. What will be the area of the square made from the rope?(in cm2)
A)
B)
C)
D)
289
324
400
456
Question 6

15. The surface area of a cube whose volume is 64, is _____.
A)
B)
C)
D)
32
64
96
108
Question 7

16. Volume of a sphere whose surface area is 144π cm2 (in cm3), is ________.
A)
B)
C)
D)
256π
288π
325
None of these
Question 8

17. The length, width and height of a rectangular solid are in the ratios 5 : 4 : 2.
If total surface area is 4864m2, then height of the solid is _____________.
A)
B)
C)
D)
16
20
24
28
Question 9

18. Length of cloth in meters which is 2.5 m wide is required to make a conical
tent with base radius of 7 m and height of 24 m is _________.
A)
B)
C)
D)
90π
110π
125π
140π
Question 10

19. The base of a rectangular tank is 12 feet long and 8 feet wide, and height of
the tank is 30 inches. If water is pouring into the tank at the rate of 2 cubic
feet per second, then time taken required to fill the tank is _______.
A)
B)
C)
D)
1 min
2 min
5 min
7 min
Question 11

20. A rectangular container with dimensions 4 inches, 9 inches, 10 inches is
kept into a cylindrical container with a diameter of 6 inches. Assuring the
milk does not overflow the container, find the height(in inches)to which the
milk will reach high?
A)
B)
C)
D)
15/π
25
30/π
40/π
Question 12

21. Ratio of the total surface area to the lateral surface area of a cylinder with
base radius 60 cm and height 40 cm is ______.
A)
B)
C)
D)
2:3
5:2
6:7
None of these
Question 13

22. The diameter of a copper sphere is 12 cm. The sphere is melted and drawn
into a long wire of uniform circular cross section. If length of the wire is 72
cm, then radius of wire is _________ cm.
A)
B)
C)
D)
4
3
2
None of these
Question 14

23. A spherical ball, 12 cm in diameter, is melted and cast into a conical mould,
the base of which is 24 cm in diameter. What is the height of the cone?( in
cm)
A)
B)
C)
D)
6
12
15
None of these
Question 15

24. THANK YOU