**Mensuration Questions for RRB Group-D Set-2 PDF**

Download Top-15 RRB Group-D Mensuration Questions PDF. RRB GROUP-D Mensuration set-2 questions based on asked questions in previous exam papers very important for the Railway Group-D exam.

Download Mensuration Questions for RRB Group-D set-2 PDF

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**Question 1: **Find the length of inradius of triangle of sides 3,4 and 5.

a) 1

b) 2

c) 3

d) 4

e) None of these

**Question 2: **Find the area of the trapezium with the parallel sides of length 7 cm and 8 cm and height 18 cm?

a) 135 $cm^2$

b) 120 $cm^2$

c) 150 $cm^2$

d) 270 $cm^2$

e) 250 $cm^2$

**Question 3: **If the diagonal of the rectangle is of length $\sqrt{41}$ cm and the area is equal to 20 $cm^2$, find the perimeter of rectangle?

a) 15 cm

b) 6 cm

c) 9 cm

d) 18 cm

e) 24 cm

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**Question 4: **There is a solid cube of side 10 cm. An ant starts at one corner of the cube and travels to the diagonally opposite corner. The ant travels in such a way that it covers the least distance. What is the distance covered by the ant?

a) $30\ cm$

b) $10\sqrt2\ cm$

c) $10\sqrt5\ cm$

d) $(10 + 10\sqrt2)\ cm$

e) $10\sqrt3\ cm$

**Question 5: **The area of a rectangular cardboard is 40 $cm^2$, with one side equal to 8 cm. If a circle is drawn on the largest square piece that can be cut from the cardboard, what is the area of the circle?

a) $2.25\pi\ cm^2$

b) $4.25\pi\ cm^2$

c) $6.25\pi\ cm^2$

d) $8.25\pi\ cm^2$

e) Cannot be determined

**Question 6: **Find the volume of the cone of radius 9cm and slant height 15cm?

a) 1019$cm^2$

b) 1257$cm^2$

c) 1143$cm^2$

d) 1087$cm^2$

e) 1197$cm^2$

**Question 7: **Find the area of the square if the maximum area of the circle which can be inscribed in the square is 154 square units.

a) 169 square units

b) 144 square units

c) 196 square units

d) 225 square units

e) None of these.

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**Question 8: **The diagonal of a rectangle is $4\sqrt5$ cm and the area is 32 $cm^2$. What is the perimeter of the rectangle ?

a) 18 cm

b) 36 cm

c) 12 cm

d) 24 cm

e) 16 cm

**Question 9: **Find the area of the square if its perimeter is equal to that of triangle of sides 8cm, 10cm, 6cm.

a) 49

b) 16

c) 25

d) 36

e) None of these.

**Question 10: **A cardboard of dimension 24cm x 16cm is converted into an open box by cutting off squares of side 6cm from all four sides and folding it. What is the volume of the open box ?

a) 2304 cm$^2$

b) 384 cm$^3$

c) 288 cm$^3$

d) 200 cm$^3$

e) 1080 cm$^3$

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**Question 11: **A room is 12m long and 8m broad. The area of the 4 walls of the room is 48m$^2$ more than the sum of areas of the floor and the ceiling. Find the volume of the room ?

a) 600m$^2$

b) 476m$^2$

c) 450m$^2$

d) 576m$^2$

e) 400m$^2$

**Question 12: **Find the area of the rhombus of diagonal lengths 12cm and 14cm.

a) 76

b) 60

c) 72

d) 92

e) 84

**Question 13: **A cylindrical tank has base radius of 3.5m and height of 10m. If a tap fills the tank at the rate of $2m^3$ per minute then how much time would it take to fill an empty tank?

a) 2 hours 50 mins

b) 2 hours 55.5 mins

c) 3 hours 12.5 mins

d) 3 hours 37.5 mins

e) None of the above

**Question 14: **Find the area of the trapezium if its parallel sides are of length 13cm and 7 cm respectively and the distance between the parallel sides is 5cm?

a) 20

b) 40

c) 70

d) 60

e) 50

**Question 15: **Find the value of the exterior angle to B in an isosceles triangle ABC with AB = AC, if Angle A = 100 degrees.

a) 40 degrees

b) 100 degrees

c) 140 degrees

d) 110 degrees

e) 90 degrees

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**Answers & Solutions:**

**1) Answer (A)**

Area = r*s =$\sqrt{s(s-a)(s-b)(s-c)}$

s = (3+4+5)/2 = 6

6*r = $\sqrt{6(6-3)(6-4)(6-5)}$

6*r = 6

r = 1

**2) Answer (A)**

Area of trapezium = 0.5(Sum of parallel sides)(Height)

= 0.5(7+8)(18) = 15*9 = 135 $cm^2$

**3) Answer (D)**

Let the length and the breadth be l and b respectively.

$\sqrt{l^2+b^2} = \sqrt{41}$

$l^2+b^2 = 41$

lb = 20

2lb = 40

$l^2+b^2+2lb = 41+40$

$(l+b)^2 = 81$

l+b = 9

2(l+b) = 18 cm

**4) Answer (C)**

Let the ant start from point A. It has to reach point E. The ant will travel the least distance when it travels along AG – GE, Here, AE forms the diagonal of the rectangle AFED if the cube is cut along AD and the surface ABCD is lifted to make it level with BFEC. In this case, AF = 20 cm and FE = 10 cm. So, the length of the diagonal is $\sqrt{10^2 + 20^2}$ = $10\sqrt5\ cm$

**5) Answer (C)**

One side of the rectangle is 8 cm and the area is 40 $cm^2$. So, the other side is 5 cm. So, the largest square that can be cut out of the rectangle is a square with side 5 cm.

So, the diameter of the circle inscribed in that square is 5 cm

Area of the circle = $\pi * r^2 = \pi * 2.5^2 = 6.25\pi\ cm^2$

**6) Answer (A)**

$r^2+h^2 = l^2$

$9^2+h^2 = 15^2$

h = 12

Volume = (1/3)*(22/7)*9*9*12 =$1019cm^2$

**7) Answer (C)**

Let the side of the square be x.

Diameter of the circle = x

(22/7)*x/2*x/2 = 154

$x^2$ = 7*7*4

x = 14

Area of the square = 14*14 = 196 square units.

**8) Answer (D)**

Given,diagonal of rectangle = $\sqrt{l^2 + b^2} = 4\sqrt5 = \sqrt{80} $

also given, lb = 32

$(l + b)^2 = l^2 + b^2 + 2lb = 80 + 2\times32 = 144$

=> l + b = 12

thus, perimeter = 2(l + b) = 24 cm

**9) Answer (D)**

Perimeter of square = 4a

4a = 8+10+6 = 24

a = 6

Area of square =$a^2$ = 6*6 = 36

**10) Answer (C)**

Length of the open box = (24 – 2×6 ) = 12 cm

Breadth of the open box = (16 – 12) = 4 cm

Height of the open box = 6 cm

Thus, volume of the open box = 12 x 4 x 6 = 288 cm$^3$

**11) Answer (D)**

area of 4 walls = 2(lh) + 2(bh)

area of floor + ceiling = 2lb = 2x12x8 = 192m

Given, 2lh + 2bh = 192 + 48

12h + 8h = 120

thus, h = 6m

∴: the volume of the room = lxbxh = 12x8x6 = 576m$^2$

**12) Answer (E)**

Area of the rhombus =$\frac{1}{2}*12*14 = 84$

**13) Answer (C)**

Volume of cylindrical tank = $\pi r^2 h$ = $\frac{22}{7}* 7/2 * 7/2 * 10$ =385 $m^3$.

Hence, time taken =385/2 minutes = 192.5 minutes = 3 hours 12.5 mins

**14) Answer (E)**

Let the parallel sides be of length 13cm and 7cm.

Area =$\frac{1}{2}(13+7)(5) = 50$

**15) Answer (C)**

Since AB = AC, Angle B = Angle C = x

100+x+x = 180

x = 40 degrees

Exterior Angle to B = Angle A + Angle C

Exterior Angle to B = 100 + 40 = 140 degrees

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