Mensuration is an important part of the Quantitative aptitude section for most of the bank exams. Mensuration is the branch of geometry that deals with the measurement of area, length, or volume in 2D and 3D shapes. The 2D shapes can be drawn in a plane like square, rectangle, triangle, circle, etc. … Mensuration includes computation using mathematical formulas and algebraic equations. Mensuration is a division of mathematics that studies geometric figure calculation and its parameters such as area, length, volume, lateral surface area, surface area, etc. It outlines the principles of calculation and discusses all the essential equations and properties of various geometric shapes and figures. A 2D diagram is a shape laid down on a plane by three or more straight lines or a closed segment. Such forms do not have width or height; they have two dimensions-length and breadth and are therefore called 2D shapes or figures. Of 2D forms, area (A) and perimeter (P) is to be determined. A 3D shape is a structure surrounded by a variety of surfaces or planes. These are also considered robust types. Unlike 2D shapes, these shapes have height or depth; they have three-dimensional length, breadth, and height/depth and are thus called 3D figures. 3D shapes are made up of several 2D shapes. Often known as strong forms, volume (V), curved surface area (CSA), lateral surface area (LSA), and complete surface area (TSA) are measured for 3D shapes.
There are 10 basic mensuration formulas in Mathematics out of which, 5 are for 2D figures and 5 are for 3D figures. Q3: What are the topics in mensuration? Mensuration deals with obtaining the perimeter, area, and volume of different kinds of geometric figures. Both 2D and 3D figures are included in mensuration. Dear Aspirants, Our IBPS Guide team is providing new series of Quants Questions for competitive exams so the aspirants can practice it on a daily basis. These questions are framed by our skilled experts after understanding your needs thoroughly. Aspirants can practice these new series of questions daily to familiarize themselves with the exact exam pattern and make their preparation effective.
Mensuration For Competitive Exam (FAQ)
1) What is Mensuration?
Ans. Mensuration is the branch of geometry that deals with the measurement of area, length, or volume in 2D and 3D shapes. The 2D shapes can be drawn in a plane like square, rectangle, triangle, circle, etc. … Mensuration includes computation using mathematical formulas and algebraic equations
2) What are the two types of mensuration?
Ans. There are two types of Mensuration: 2D Mensuration and 3D Mensuration.
- The 2D figures have only two dimensions, which are primarily length and width. There is no height or depth to the two-diMensional figure. …
- The three dimensions of 3D figures are length, breadth, and height or depth.
Start Quiz
1) The ratio of the radius of the circle and the side of the square is 3:5 and the circumference of the circle is 132 cm, then find the perimeter of the square?
A.180 cm
B.300 cm
C.140 cm
D.210 cm
E.None of these
2) Perimeter of the square is 48 cm and the side of the square is 75% of the length of the rectangle whose perimeter is equal to the perimeter of the square. What is the area of the rectangle?
A.144 cm2
B.140 cm2
C.136 cm2
D.128 cm2
E.132 cm2
3) The ratio of the length and breadth of the rectangle is 5:4 and the area of the rectangle is 500 m2 and the side of the square is 5 m more than the length of the rectangle. Find the perimeter of the square.
A.120 m
B.150 m
C.200 m
D.180 m
E.None of these
4) Circumference of the circle is 88m and the ratio of the length and breadth of the rectangle is 7:5 and the length of the rectangle is equal to the radius of the circle. Find the perimeter of the rectangle.
A.55m
B.48m
C.42m
D.38m
E.None of these
5) The side of the square is 5 cm more than the height of the cylinder and the perimeter of the square is 40 cm. If the volume of the cylinder is 770 cm3, then find the radius of the cylinder?
A.7 cm
B.14 cm
C.9 cm
D.12 cm
E.None of these
6) If the area of a square is 576 cm2 and the length of a rectangle is equal to the side of the square and the breadth of the rectangle is 18 cm and the perimeter of the rectangle is 4 cm less than the circumference of the circle, then what is the area of the circle?
A.1232 cm2
B.1386 cm2
C.616 cm2
D.154 cm2
E.308 cm2
7) The radius of a cylinder is equal to the side of a square and the height of the cylinder is 5 cm. If the volume of the cylinder is 3080 cm3, then find the perimeter of the square?
A.56 cm
B.44 cm
C.32 cm
D.72 cm
E.None of these
8) If the ratio of the total surface area of cylinder to its curved surface area is 5:4, then radius of the cylinder is what percentage less than height of the cylinder?
A.75%
B.50%
C.42%
D.25%
E.None of these
9) The side of the square is equal to the breadth of the rectangle and the length of the rectangle is 25% more than its breadth. If the perimeter of the rectangle is 90 cm, then what is the difference between the area of the square and rectangle?
A.100 cm2
B.180 cm2
C.120 cm2
D.150 cm2
E.160 cm2
10) The circumference of the semicircle is 108 cm. If the radius of the semicircle is equal to the radius of the cylinder and the curved surface area of the cylinder is 1056 cm2, then find the volume of the cylinder?
A.8316 cm3
B.12474 cm3
C.11088 cm3
D.9702 cm3
E.None of these
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Answers :
1) Answer: C
The radius of the circle=r
2*22/7*r=132
r=132*7/22*1/2
r=21 cm
The side of the square=21*5/3=35 cm
The perimeter of the square=4*35=140 cm
2) Answer: D
4a = 48
a = 12 cm
Length of the rectangle = 4/3 * 12 = 16 cm
Breadth of the rectangle = 48/2 – 16 = 8 cm
Area of the rectangle = 16 * 8 = 128 cm2
3) Answer: A
Length of the rectangle = 5x
Breadth of the rectangle = 4x
5x * 4x = 500
x2 = 25
x = 5 m
Side of the square = 5*5 + 5 = 30 m
Perimeter of the square = 4a = 4*30 = 120 m
4) Answer: B
Circumference of the circle = 88m
2πr = 88
r = 14m
Length of the rectangle = 14m
Breadth of the rectangle = 14*5/7 = 10m
Perimeter of the rectangle = 2(l+b) = 2(14+10) = 48m
5) Answer: A
The side of the square=40/4=10 cm
The height of the cylinder=10-5=5 cm
22/7*r2*5=770
r2=49
r=7 cm
6) Answer: C
Side of the square = (576)(1/2)= 24 cm
Perimeter of the rectangle = 2 * (24 + 18) = 84 cm
Circumference of the circle = 84 + 4 = 88 cm
Radius of the circle = 88 * 7/22 * 1/2 = 14 cm
Area of the circle = 22/7 * 14 * 14 = 616 cm2
7) Answer: A
Let the radius of the cylinder=x cm
The volume of the cylinder=3080 cm3
22/7*x*x*5=3080
x2=196
x=14
The perimeter of the square=4*14=56 cm
8) Answer: A
Let the radius of the cylinder = r
Height of the cylinder = h
Total surface area of cylinder = 2πr(r+h)
Curved surface area of cylinder = 2πrh
2πr(r+h) / 2πrh = 5/4
4r+4h = 5h
4r= h
Required % = (h-r)/h*100 = (4r-r)/4r * 100 = 75%
9) Answer: A
Ratio of the length to breadth of the rectangle = 125:100 = 5:4
(5x + 4x) * 2 = 90
x = 5
Length of the rectangle = 5 * 5 = 25 cm
Breadth of the rectangle = 4 * 5 = 20 cm
Side of the square = 20 cm
Area of the square = 20 * 20 = 400 cm2
Area of the rectangle = 25 * 20 = 500 cm2
Difference = 500 – 400 = 100 cm2
10) Answer: C
r * (22/7 + 2) = 108
r = 21 cm
1056 = 2 * 22/7 * 21 * h
Height of the cylinder = 8 cm
Volume of the cylinder = 22/7 * 21 * 21 * 8
= 11088 cm3
Start Quiz
11) If the length of the rectangle increased by 25% and the breadth of the rectangle is decreased by 10%, then find the area of the rectangle will be increased or decreased?
A.10% decreased
B.12.5% increased
C.15% increased
D.10.5 increased
E.7.5% decreased
12) The length of the rectangle is 50% more than its breadth and the area of the rectangle is 1176 cm2. If the perimeter of the rectangle is 5x cm and the side of the square is x cm, then find the perimeter of the square?
A.120 cm
B.116 cm
C.112 cm
D.108 cm
E.100 cm
13) Perimeter of the square is 48 cm and the side of the square is 75% of the length of the rectangle whose perimeter is equal to the perimeter of the square. What is the area of the rectangle?
A.144 cm2
B.140 cm2
C.136 cm2
D.128 cm2
E.132 cm2
14) The circumference of the semi-circle is 360cm. If the side of the square is 3/5th of diameter of the semi-circle, then what is the perimeter of the square?
A.332 cm
B.336 cm
C.340 cm
D.344 cm
E.348 cm
15) If the ratio of length, breadth and height of a cuboid is 3:2:5 and the total surface area of the cuboid is 248 cm2 and the length of the cuboid is equal to the breadth of the rectangle and length of the rectangle is 4 cm more than its breadth, then find the area of the rectangle?
A.60 cm2
B.150 cm2
C.120 cm2
D.90 cm2
E.None of these
16) Total surface area (in cm2)of a cube is 75% of volume (in cm3)of that cube. Find the total surface area of the cube?
A.390 cm2
B.384 cm2
C.375 cm2
D.387 cm2
E.Cannot be determined
17) The area of the circle is 616 cm2 and the radius of the cone is equal to the radius of the circle. If the ratio of the height and radius of the cone is 6:7, then what is the volume of the cone?
A.3696 cm3
B.616 cm3
C.2464 cm3
D.1232 cm3
E.None of these
18) Diameter of the circle is equal to the breadth of the rectangle and the ratio of the length to breadth of the rectangle is 5:4. If the perimeter of the rectangle is 126 cm, then what is the difference between the area of the circle and rectangle?
A.304 cm2
B.294 cm2
C.364 cm2
D.324 cm2
E.384 cm2
19) The curved surface of cone is 180∏ cm2 and the radius of the cone is 12 cm. Ratio of the radius of cone to cylinder is 6:7 and the height of cylinder is 3 cm more than the height of the cone, then find the volume of the cylinder?
A.7592 cm3
B.7692 cm3
C.7892 cm3
D.7392 cm3
E.7492 cm3
20) If the radius of the circle is increased by 20%, then the area of the circle is increased by 271.04 cm2. Find the circumference of the circle?
A.44 cm
B.66 cm
C.88 cm
D.132 cm
E.None of these
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Answers :
11) Answer: B
Original area of rectangle = 100
New area = 100 * 125/100 * 90/100 = 112.5
Area of rectangle is 12.5% increased
12) Answer: C
Breadth of the rectangle = 2a
Length of the rectangle = 150/100 * 2a = 3a
2a * 3a = 1176
a = 14 cm
Perimeter of the rectangle = 2 * (42 + 28) = 140 cm
Side of the square = 140/5 = 28 cm
Perimeter of the square = 4 * 28 = 112 cm
13) Answer: D
4a = 48
a = 12 cm
Length of the rectangle = 4/3 * 12 = 16 cm
Breadth of the rectangle = 48/2 – 16 = 8 cm
Area of the rectangle = 16 * 8 = 128 cm2
14) Answer: B
Circumference of the semi-circle = 360cm
r(π+2) = 360
r (22/7 +2) =360
Therefore, radius of the semi-circle = 70cm
Diameter of the semi-circle = 140cm
Side of the square = 3/(5 ) (140) = 84cm
Perimeter of the square = 4a = 4*84 = 336 cm
15) Answer: A
248 = 2 * (3x * 2x + 2x * 5x + 5x * 3x)
31x2 = 124
x2 = 4
x = 2
Breadth of the rectangle = 2 * 3 = 6 cm
Length of the rectangle = 6 + 4 = 10 cm
Area of the rectangle = 6 * 10 = 60 cm2
16) Answer: B
Let side of the cube = ‘a’ cm
So, total surface area of the cube = 6a2 cm2
And volume of the cube = a3 cm3
From the question:
6a2 = a3 * (75/100)
6a2 = 3a3/4
a = 8 cm
So, total surface area of the cube = 6 * 8 * 8 = 384 cm2
17) Answer: C
22/7 * r * r = 616cm2
Radius of the circle = 14 cm= Radius of the cone
Height of the cone = 6/7 * 14 = 12 cm
Volume of the cone = 1/3 * 22/7 * 14 * 14 * 12
= 2464 cm3
18) Answer: C
2 * (5x + 4x) = 126
x = 7
Breadth of rectangle = 7 * 4 = 28 cm
Diameter of the circle = 28 cm
Radius of the circle = 28/2 = 14 cm
Area of the circle = 22/7 * 14 * 14 = 616
Area of the rectangle = 35 * 28 = 980
Difference = 980 – 616 = 364 cm2
19) Answer: D
22/7 * 12 * l = 180 * 22/7
l = 15
Height of cone = √152 – 122
= 9 cm
Radius of cylinder = 7/6 * 12 = 14 cm
Height of cylinder = 9 + 3 = 12 cm
Volume of cylinder = 22/7 * 14 * 14 * 12
= 7392 cm3
20) Answer: C
Radius of the circle = x
After increased the radius = x * 120/100 = 6x/5
22/7 * 6x/5 * 6x/5 – 22/7 * x * x = 271.04
22/7(36x2 – 25x2/25) = 271.04
11x2 = 2156
x = 14
Circumference of circle = 2 * 22/7 * 14
= 88 cm
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