**Mensuration Questions for Banking, Insurance and SSC Exams**

- What will be the area of trapezium whose parallel sides are 22 cm and 16 cm long, and the distance between them is 11 cm?

A) 209 cm^{2}

B) 282 cm^{2}

C) 265 cm^{2}

D) 179 cm^{2}

E) 302 cm^{2}

View Answer

** Option A**

Solution:

Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (22 + 16) * (11) = 209 cm^{2}

- The perimeter of a rectangle is 42 m. If the area of the square formed on the diagonal of the rectangle as its side is 1 1/12 % more than the area of the rectangle, find the longer side of the rectangle.

A) 19 m

B) 16 m

C) 9 m

D) 5 m

E) 12 m

View Answer

** Option E**

Solution:

Let the sides of the rectangle be l and b respectively.

From the given data,

âˆš(l2 + b2) = (1 + 1 1/12) lb

=> l2 + b2 = (1 + 13/12) lb = 25/12 * lb

12(l^{2} + b^{2} ) = 25 lb

Adding 24 lb on both sides

12 l^{2} + 12b^{2} + 24lb = 25 lb

12(l^{2} + b^{2} + 2lb) = 49 lb

12(l + b)^{2} = 49lb

but 2(l + b) = 42 => l + b = 21

So 12(21)^{2} = 49lb

Solve, we get lb = 108

Since l + b = 21, longer side = 12 m

- At the rate of Rs. 2 per sq m, cost of painting a rectangular floor is Rs 5760. If the length of the floor is 80% more than its breadth, then what is the length of the floor?

A) 25 m

B) 72 m

C) 67 m

D) 56 m

E) 46 m

View Answer

** Option B**

Solution:

Let the length and the breadth of the floor be l m and b m respectively.

l = b + 80% of b = l + 0.8 b = 1.8b

Area of the floor = 5760/2 = 2880 sq m

l*b = 2880 i.e., l * l/1.8 = 2880

l = 72

- A 7 m wide path is to be made around a circular garden having a diameter of 7 m. What will be the area of the path in square metre?

A) 298

B) 256

C) 308

D) 365

E) 387

View Answer

** Option C**

Solution:

Area of the path = Area of the outer circle – Area of the inner circle = Ï€{7/2 + 7}2 – Ï€ [7/2]2

= 308 sq m

- The perimeter of a rectangle of length 62 cm and breadth 50 cm is four times perimeter of a square. What will be the circumference of a semicircle whose diameter is equal to the side of the given square?

A) 36 cm

B) 25 cm

C) 29 cm

D) 17 cm

E) 16 cm

View Answer

** Option B**

Solution:

Let the side of the square be a cm.

Parameter of the rectangle = 2(62 + 50) = 224 cm Parameter of the square = 56 cm

i.e. 4a = 56

So a = 14

Diameter, d of the semicircle = 14 cm

Circumference of the semicircle = 1/2(Ï€)(r) + d

= 1/2(22/7)(7) + 14 = 25 cm

- What is the volume of a cylinder whose curved surface area is 1408 cm
^{2} and height is 16 cm?

A) 7715 cm^{3}

B) 9340 cm^{3}

C) 8722 cm^{3}

D) 7346 cm^{3}

E) 9856 cm^{3}

View Answer

** Option E**

Solution:

2Ï€rh = 1408, h = 16

Solve both, so r = 14

Volume = Ï€ r^{2}h = (22/7) * 14 * 14 * 16 = 9856

- A cone with diameter of its base as 30 cm is formed by melting a spherical ball of diameter 10 cm. What is the approximate height of the cone?

A) 6 cm

B) 3 cm

C) 2 m

D) 5 cm

E) None of these

View Answer

** Option C**

Solution:

Radius of cone = 30/2 = 15, radius of ball = 10/2 = 5

Volumes will be equal, so

(1/3) Ï€ r^{2}h = (4/3) Ï€ R^{3}

15^{2}h = 4* 5^{3}

So h = 2.2

- A cylinder whose base of circumference is 6 m can roll at a rate of 3 rounds per second. How much distance will the cylinder cover in 9 seconds?

A) 125 m

B) 162 m

C) 149 m

D) 173 m

E) 157 m

View Answer

** Option B**

Solution:

Distance covered in one round = 2 x Ï€ x r = 6 m

Distance covered in 1 second = 3 x 6 = 18 m

So distance covered in 9 seconds = 18Ã—9= 162m

- A container is formed by surmounting a hemisphere on a right circular cylinder of same radius as that of hemisphere. If the volume of the container is 576Ï€ m
^{3} and radius of cylinder is 6 m, then find the height of the container.

A) 14 m

B) 12 m

C) 20 m

D) 18 m

E) 22 m

View Answer

** Option D**

Solution:
Volume of the container = Volume of the cylinder + Volume of the hemisphere
Volume of the container = Ï€ 6^{2}h + (2/3) Ï€ 6^{3} = 576Ï€
= Ï€ 36 (h + 4) = 576Ï€
Solving we get h = 12
So the height of the container = 12 + 6 = 18 m
- The radii of two cylinders are in the ratio 3 : 2 and their curved surface areas are in the ratio 3 : 5. What is the ratio of their volumes?

A) 8 : 11

B) 5 : 9

C) 7 : 4

D) 9 : 10

E) 13 : 7

View Answer

** Option D**

Solution:

r1/r2 = 3/2 or r1 = 3/2 * r2

CSA1/CSA2 = 2Ï€r1h1/2Ï€r2h2 = 3/5

So h1/h2 = 2/5

Volume1/ Volume2 = Ï€r1^{2}h1/ Ï€r2^{2}h2 = 9/10

#### Click here to go to Quantitative Aptitude Section.

mam, ek doubt h

A,B and C can complete a work in 40% lesser time than C while B and C can complete the same work in 60% lesser time than A . if A, B and C together can complete the work in 20 days . then in how many days they alone do the work ?

A, B and C in 40% lesser time than C. So C in 40/(100-40) * 100 = 200/3% more time than A, B and C together.

So C in (1 + 200/3)% of 20 = 100/3 days.

1/A + 1/B + 3/100 = 1/20

So 1/A + 1/B = 1/50

Now

B and C can complete the same work in 60% lesser time than A:

60% lesser than A means 40/100 of A or 2A/5

1/B + 3/100 = 5/2A.

Now solve these 2 equations in A and B.

A 70 days. B 175 days. C 100/3 days

Distance covered in one round = 2 x Ï€ x r = 6 m

Distance covered in 1 second = 3 x 6 = 18 m

So distance covered in 9 seconds = 18/9 = 2m

if in 1 sec 18 m….then it should be more in 9 sec

somthing is wrong

qstn no 7

Ohh yes. 18Ã—9

ohhhk

arey ye Purani ID hai BA pe block hai….isko b delete krta hoon haha …..distract kr deti ho yar ðŸ˜€

haha,,ok padho srry distraction k liy

hmm aap bhi pdho acche see, no sorry ðŸ™‚

bye tc:)

ans wat i asked ..pls if u kno…

muje nhi pta tha

no prob…himanshu has replied

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