Mensuration Questions For Bank Clerk Prelims

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 circumference of a circle is equal to the perimeter of a square. The side of the square is 55 cm. What is double the diameter of the circle?

A.35 cm

B.120 cm

C.140 cm

D.84 cm

E.70 cm

2) If the slanting height and radius of the cone is 25 cm and 7 cm respectively, what is the volume of the cone?

A.1832 cm³ 

B.1932 cm³ 

C.1132 cm³ 

D.1232 cm³ 

E.1042 cm³ 

3) The height and radius of the cone is 24 cm and 7 cm respectively and the radius of the cylinder equal to the radius of the cone. What is the ratio of the curved surface area of the cone to total surface area of the cylinder whose height is 18 cm?

A.1:2

B.3:4

C.2:3

D.4:5

E.None of these

4) Ratio of the breadth of the rectangle and side of the square is 5:8 and the perimeter of the square is 2 cm less than the perimeter of the rectangle. If the area of the rectangle is 276 cm² less than the area of the square, then what is the area of the square?

A.225 cm²

B.576 cm²

C.484 cm²

D.Cannot be determined

E.None of these

5) If the ratio of the side of the square to radius of the cylinder is 6: 7 and the perimeter of the square is 48 cm. Height of the cylinder is 6 cm more than the side of the square. What is the volume of the cylinder?

A.11188 cm³

B.11388 cm³

C.11288 cm³

D.11088 cm³

E.None of these

6) The perimeter of a square is 84 cm. Find the volume of sphere, if the radius of the sphere is equal to the side of the square?

A.36524 cm³

B.36756 cm³

C.38808 cm³

D.41562 cm³

E.None of these

7) The perimeter of equilateral triangle is 54 cm. The side of equilateral triangle is 3 cm less than the radius of circle. Find the difference between the circumference of circle and the perimeter of equilateral triangle?

A.78 cm

B.84 cm

C.88 cm

D.72 cm

E.None of these

8) The circumference of two circles is 132 metres and 176 metres respectively. What is the difference between the area of the larger circle and the smaller circle?

A.1078 m²

B.1152 m²

C.986 m²

D.854 m²

E.None of these

9) The perimeter of a rectangular field is twice the perimeter of a square field. If side of the square field is 20 m and breadth of the rectangular field is 30m, then find the area of the rectangular field?

A.1250 m²

B.1300 m²

C.1350 m²

D.1500 m²

E.None of these

10) If the circumference of the circle is 132 cm and the radius of the circle is equal to the length of the rectangle whose perimeter is 80 cm, find the area of the rectangle?

A.369 cm²

B.379 cm²

C.399 cm²

D.389 cm²

E.None of these

 

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Answers :

1) Answer: C

The circumference of a circle is equal to the perimeter of a square = 2πr = 4a

2 * 22/7 * r = 4 * 55

r = 35

Diameter = 2r = 70

Double the diameter of the circle = 2 * 70 = 140

2) Answer: D

Height of the cone = √25² – 7² = 24 cm

Volume of the cone = 1/3πr²h

= 1/3 * 22/7 * r² * h

= 1/3 * 22/7 * 7 * 7 * 24

= 1232 cm³

3) Answer: A

Slanting height of the cone = √h² + r² = √24² + 7²

= 25 cm

CSA of Cone = 22/7 * r * l

TSA of the cylinder = 2 * 22/7 * r * (h + r)

Required ratio = 22/7 * 7 * 25 : 2 * 22/7 * 7 * (18 + 7)

= 1: 2

4) Answer: D

Perimeter of the rectangle= 2 * (l + b)

Perimeter of the square = 4 * a

Breadth of the rectangle = 5x

Side of the square = 8x

(2l + 10x ) – 4 * 8x = 2

2l – 22x = 2

l – 11x = 1

8x * 8x – l * 5x = 276

64x² – 5xl = 276

We cannot find the answer.

5) Answer: D

Perimeter of the square = 4 * a = 48 cm

Side of the square = 12 cm

Height of the cylinder = 12 + 6 = 18 cm

Radius of the cylinder = 7/6 * 12 = 14 cm

Volume of the cylinder = 22/7 * r *r * h

= 22/7 * 14 * 14 * 18

= 11088 cm³

6) Answer: C

The perimeter of a square = 84 cm

4a = 84

Side (a) = 21 cm = Radius of the sphere

Volume of sphere = (4/3) * πr³

= > (4/3) * (22/7) * 21 * 21 * 21

= > 38808 cm³

7) Answer: A

The perimeter of equilateral triangle = 54 cm

3a = 54

Side (a) = 18 cm

The side of equilateral triangle = Radius of circle – 3

Radius of circle = 18 + 3 = 21 cm

Circumference of circle = 2πr = 2 * (22/7) * 21 = 132 cm

Required difference = 132 – 54 = 78 cm

8) Answer: A

Circumference of circle1 = 132

2πr1 = 132

2*(22/7)*r1 = 132

r1 = 132*(7/44)

r1 = 21

Circumference of circle2 = 176

2πr2 = 176

2*(22/7)*r2 = 176

r2 = 176*(7/44)

r2 = 28

Required answer = πr2² – πr1² = π*(r2² – r1²)

= > (22/7)*(28² – 21²)

= > (22/7)*(28+21) (28 – 21)

= > (22/7)*(49)*(7)

= > 1078 m².

9) Answer: D

Perimeter of square field= 20*4= 80m

Perimeter of the rectangular field= 160m

Let the length of the rectangular field be x

160= 2(x+30)

160- 60= 2x

x= 50 m

Area of the rectangular field= 50*30= 1500 m²

10) Answer: C

Circumference of the circle = 2 * 22/7 * r = 132

Radius of the circle = 21 cm

Perimeter of the rectangle = 2 * (l + b)

Length of the rectangle = 21 cm

80 = 2 * (21 + b)

b = 19 cm

Area of the rectangle = l * b = 19 * 21 = 399 cm²

Start Quiz

 

11) If the length of the rectangle is increased by 20% and the breadth of the rectangle is decreased by 15%, then find the  percentage increase or decrease of the area of the rectangle?

A.1% decrease

B.2% increase

C.5% decrease

D.4% increase

E.None of these

12) Circumference of the circle is 88 cm. If the radius of the circle is seven-fifth of side of the square whose perimeter is 10 cm more than the perimeter of the equilateral triangle. What is the area of the equilateral triangle?

A.25√3 cm²

B.26√3 cm²

C.27√3 cm²

D.28√3 cm²

E.None of these

13) The perimeter of a square is 84 cm. Find the volume of sphere, if the radius of the sphere is equal to the side of the square?

A.36524 cm³

B.36756 cm³

C.38808 cm³

D.41562 cm³

E.None of these

14) If the ratio of the side of the cube to side of the square is 1:2 and the ratio of the length to breadth of the rectangle is 5:4 and the area of the rectangle is 80cm². If the perimeter of the rectangle is equal to the area of the square, then find the volume of the cube?

A.64 cm³ 

B.8 cm³

C.25 cm³

D.27 cm³

E.None of these

15) The ratio of Curved Surface Area to Total Surface Area of Cylinder is 3: 7. If the Curved Surface Area of the Cylinder is 3696 m², find the height of the cylinder.

A.23m

B.21m

C.27m

D.29m

E.None of these

16) The ratio of the radius of the cylinder and sphere is 1:2 and the height of the cylinder is 14cm. If the curved surface area of the cylinder is 616cm², then what is the difference between the volume of the cylinder and the surface area of the sphere?

A.308

B.402

C.317

D.423

E.None of these

17) The base of the parallelogram is equal to the side of a square whose area is 441 cm². If the height of the parallelogram is 22 cm, find the area of the parallelogram.

A.484 cm²

B.924 cm²

C.441 cm²

D.231 cm²

E.None of these

18) If the length of the cuboid increased by 30%, height of the cuboid is increased by 10% and the breadth of the cuboid is decreased by 40%. Then find the volume will be increased or decreased by.

A.14.2% increased

B.12.5% decreased

C.8.2% increased

D.13.6% decreased

E.None of these

19) Ratio of the side of the square to breadth of the rectangle is 2:1. If the perimeter of the rectangle is 48 cm and the length of the rectangle is double of the breadth of the rectangle, then what is the area of the square?

A.196 cm²

B.256 cm²

C.225 cm²

D.324 cm²

E.None of these

20) The circumference of a circle is one-third of the perimeter of a rectangle. The area of the circle is 2464 sq. m. What is the area of the rectangle, if the breadth of the rectangle is 120 m?

A.18560 sq. m

B.17280 sq. m

C.16720 sq. m

D.19340 sq. m

E.None of these

 

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Answers :

11) Answer: B

Let initial Area of the rectangle = 100

100 * 120/100 * 85/100 = 102

Area = 2% increase

12) Answer: A

Circumference of the circle = 2 * 22/7 * r

88 = 2 * 22/7 * r

Radius of the circle = 14 cm

14 = 7/5 * a

a = 10cm

Perimeter of the square = 4 * 10 = 40 cm

Perimeter of the equilateral triangle = 40 – 10 = 30 cm

Side of the equilateral triangle = 3 * a = 30

Side of the equilateral triangle = 10 cm

Area of the equilateral triangle = √3/4 * 10 * 10

= 25√3 cm²

13) Answer: C

The perimeter of a square = 84 cm

4a = 84

Side (a) = 21 cm = Radius of the sphere

Volume of sphere = (4/3) * πr³

= > (4/3) * (22/7) * 21 * 21 * 21

= > 38808 cm³

14) Answer: D

5x*4x=80

x=2

Now, perimeter of the rectangle=2(9*2)=36cm

Thus, side of the square=6cm

And, side of the cube=3cm

Hence, volume of the cube=3*3*3=27cm³

15) Answer: B

Curved Surface Area of Cylinder = 2πrh

Total Surface Area of Cylinder = 2πr (h + r)

According to question,

2πrh/(2πr (h + r)) = 3/7

h/(h + r) = 3/7

7h = 3h + 3r

4h = 3r

r = 4h/3

And, Curved Surface Area of Cylinder = 3696m²

2πrh = 3696

2π × 4h/3 × h = 3696

h² = 21× 21

h = 21 m.

16) Answer: A

616 = 2 * 22/7 * 14 * r

R = 7cm

Radius of the sphere=2/1 * 7 = 14cm

Volume of the cylinder=22/7 * 7 * 7 * 14 = 2156

Surface area of the sphere = 4 * 22/7 * 14 * 14 = 2464

Difference = 2464 – 2156 = 308

17) Answer: E              

Area of the square = a²

Side a = 21 cm

Area of the parallelogram = b * h

Here b = 21 cm

h = 22 cm

Area of the parallelogram = 21 * 22 = 462 cm²

18) Answer: E

Let the initial volume of the cuboid =100

Increased or decreased volume of the cuboid =100 * 130/100 * 110/100 * 60/100

= 85.8

= 14.2% decreased

19) Answer: B

Side of the square = 2x

Breadth of the rectangle = x

Length of the rectangle = 2x

2 * (x + 2x) = 48

x = 8

Side of the square = 2 * 8 = 16 cm

Area of the square = 16 * 16 = 256 cm²

20) Answer: B

Area of a circle = πr²

2464 = 22r²/7

2464*(7/22) = r²

r² = 784

r = 28 m

Circumference of a circle = 2πr = 2*(22/7)*28 = 176 m

Perimeter of the rectangle = 3*176 = 528 m

528 = 2*(l + 120)

264 = l + 120

l = 264 – 120

l = 144

Area of the rectangle = 144*120 = 17280 sq. m

 

Start Quiz

 

21) The circumference of the circle is 176 m and the radius of the circle is equal to the side of the equilateral triangle. Find the area of equilateral triangle?

A.256√3sq m

B.144√3sq m

C.184√3sq m

D.196√3sq m

E.None of these

22) Ratio of the radius of the cone to circle is 1: 2 and the curved surface area of the cone is 396 cm². If the circumference of the circle is 88 cm, then find the height of the cone?

A.3√11 cm

B.4√11 cm

C.5√11 cm

D.6√11 cm

E.None of these

23) If the cost of fencing the circular plot at Rs. 65 per meter is Rs. 8580, then find the area of the plot?

A.1524 Sq m

B.1278 Sq m

C.1386 Sq m

D.1452 Sq m

E.None of these

24) One of the angles of the quadrilateral is 69^◦. The ratio of the remaining angles is 33:20:44. What is the difference between 2^nd largest angle and smallest angle?

A.39

B.60

C.69

D.45

E.None of these

25) The breadth of a rectangle is 150% of the radius of a circle. The ratio of the length to breadth of the rectangle is 7:3. If the area of the circle is 616m², then find the perimeter of the rectangle.

A.120m

B.140m

C.150m

D.110m

E.160m

26) Area of a square is 784m². Find the surface area of a sphere whose radius is 125% of the side of the square.

A.14400m²

B.15400m²

C.13600m²

D.18400m²

E.16400m²

27) The ratio of length and breadth of the rectangle is 3: 2 and the perimeter of the rectangle is 100 Sq cm. Find the diagonal of the square, whose area is 200 Sq cm more the area of the rectangle?

A.50 cm

B.45 cm

C.55 cm

D.40 cm

E.None of these

28) The total area of a circle and rectangle is 2386 Sq cm. The radius of the circle is 21 cm. Find the sum of circumference of circle and perimeter of rectangle, if length of the rectangle is 40 cm?

A.248 cm

B.316 cm

C.284 cm

D.262 cm

E.None of these

29) The radius of the semicircle is equal to the half the side of the square, whose area is 1764 Sq. Cm. Find the perimeter of the semicircle?

A.102 cm

B.108 cm

C.110 cm

D.120 cm

E.None of these

30) If the ratio between the radius of two cylinders A and B is 2 : 3 and the volume of those cylinders is in the ratio of 2 : 7, then find the ratio of height of two cylinders A and B?

A.11 : 13

B.7 : 11

C.5 : 8

D.9 : 14

E.None of these

 

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Answers :

21) Answer: D

The circumference of the circle = 176 m

Given,

2 * (22/7) * r = 176

r = 176 * (7/44) = 28 m = Side of equilateral triangle (a)

The area of equilateral triangle

= >(√3 / 4) * a²

= >(√3 / 4) * 28 * 28

= > 196√3 sq m

22) Answer: C

Circumference of the circle = 2 * 22/7 * r

88 = 2 * 22/7 * r

r = 14 cm

Radius of the circle = 14 cm

Radius of the cone = 14 * ½ = 7 cm

CSA of the cone = πrl = 22/7 * r * l

396 = 22/7 * 7 * l

l = 18 cm

Height of the cone = √(18² – 7²)

= 5√11 cm

23) Answer: C

Circumference of circle = 2 * (22/7) * r = (8580 /65)

= > 2 * (22/7) * r = 132

= > r = (132 * 7) / 44 = 21 cm

The area of plot = πr² = (22/7) * 21 * 21 = 1386 Sq m

24) Answer: A

Total angle of quadrilateral = 360

1 angle = 69

Sum of remaining angles = 360 – 69 = 291

33x + 20x + 44x = 291

x = 3

Angles = 69,99,60,132

Required answer = 99 – 60=39

25) Answer: B

Area of circle = 616

(22/7)*r² = 616

r = 14

Breadth of rectangle = (150/100)*14 = 21m

Length of rectangle = 21*(7/3) = 49

Perimeter of rectangle = 2(49+21) = 140m

26) Answer: B

(Side)² = 784

Side = 28

Radius of sphere = (125/100)*28 = 35

Surface area of sphere = 4πR² = 4*(22/7)*35*35 = 4*22*5*35 = 15400m²

27) Answer: D

The ratio of length and breadth of the rectangle = 3: 2 (3x, 2x)

Given,

2 * (3x + 2x) = 100

10x = 100

x = 10

The length and breadth of the rectangle = 30 cm and 20 cm

The area of rectangle = lb = 30 * 20 = 600 Sq cm

The area of square = 600 + 200 = 800 Sq cm = (1/2) * Diagonal²

Diagonal² = 1600

Diagonal = 40

The diagonal of the square = 40 cm

28) Answer: D

Πr² + lb = 2386

(22/7) * 21 * 21 + 40b = 2386

1386 + 40b = 2386

40b = 2386 – 1386

40b = 1000

b = 25 cm

Circumference of circle = 2πr = 2 * (22/7) * 21 = 132 cm

Perimeter of rectangle = 2 * (l + b) = 2 * (40 + 25)

= > 2 * 65 = 130 cm

Required answer = 132 + 130 = 262 cm

29) Answer: B

Area of square = a² = 1764

Side (a) = 42 cm

Radius of the semicircle = (1/2) * 42 = 21 cm

Perimeter of semicircle = πr + d

= > 21π + 42 cm

= >108 cm

30) Answer: D

The volume of cylinder =πr²h

Given,

= > [π * (2x)² * h1] / [π * (3x)² * h2] = 2/7

= > h1 / h2 = 9/14

The ratio of height of two cylinders A and B = 9 : 14

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