# Mensuration Questions for RRB Group-D PDF

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## Mensuration Questions for RRB Group-D PDF

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

Question 1: Find the area of the rhombus of diagonal lengths 12cm and 14cm.

a) 76

b) 60

c) 72

d) 92

e) 84

Question 2: Find the length of the rectangle , if the perimeter of the rectangle is same as perimeter of triangle with sides 23cm, 11cm, 16cm and the length of the rectangle is 1.5 times the breadth?

a) 5

b) 10

c) 8

d) 15

e) 20

Question 3: 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 4: If the height of a triangle is increased by 10% and base is decreased by 10%, then its area would be 198 sq-cm. What was the original area?

a) 100 sq-cm

b) 160 sq-cm

c) 180 sq-cm

d) 200 sq-cm

e) None of these

Question 5: Find the total surface area of the solid hemispehere of radius 7cm?

a) 308

b) 462

c) 374

d) 542

e) None of these

Question 6: In the given figure AB is parallel to CD and XY is a transversal as shown. If Angle XEA = 100 degrees, find the value of angle XFD?

a) 60 degrees

b) 70 degrees

c) 80 degrees

d) 90 degrees

e) 100 degree

Question 7: In the given figure AB is parallel to CD and XY is a transversal as shown. If Angle XEB = 110 degrees, find the value of Angle DFY?

a) 70 degrees

b) 80 degrees

c) 90 degrees

d) 100 degrees

e) 110 degrees

Question 8: Find the sum of all the angles of a hexagon?

a) 360 degrees

b) 720 degrees

c) 540 degrees

d) 180 degrees

e) 270 degrees

Question 9: In a triangle ABC, find the value of the exterior angle to A if the exterior angle to B and C measure 120 and 150 degrees respectively?

a) 140 degrees

b) 100 degrees

c) 120 degrees

d) 90 degrees

e) 110 degrees

Question 10: A circle is inscribed in a square of side 8 cm. What is the ratio of the area of the circle to its circumference?

a) 2:1

b) 4:3

c) 8:1

d) 1:2

e) 4:1

Question 11: A square and a rectangle have the same area. If the breadth of the rectangle is 4.5 metres, side of the square is 5 metres, what is the length of the rectangle?

a) 4.56

b) 5.56

c) 6.56

d) 7.56

e) None of the above

Question 12: What is the area of a square whose diagonal is 52 metres?

a) 1160

b) 1260

c) 1352

d) 1460

e) None of the above

Question 13: A square has the side equal to the diameter of a circle. If the perimeter of the square is 20 metres, what is the perimeter of the circle?

a) 14.7

b) 15.7

c) 16.7

d) 17.7

e) None of the above

Question 14: What would be the area of a circle whose circumference is 35.2 cm?

a) 67.22 sq cm

b) 75.54 sq cm

c) 98.56 sq cm

d) 86.75 sq cm

e) None of these

Question 15: The length of a rectangle is equal to the side of a square. The breadth is one thirds of the length. What is the ratio of the area of the square to that of the rectangle?

a) 3:1

b) 1:3

c) 9:1

d) 1:9

e) None of the above

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

Let the breadth of the rectangle be x.
Length = 1.5x
2(x+1.5x) = 23+11+16 = 50
2.5x = 25
x = 10
Length = 1.5*10 = 15

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

Let the base and height be b and h respectively. Hence, the original area is = 1/2*b*h. After changing the base and height, area= 1/2 * (0.9b) * (1.1h) = 0.99 (1/2*b*h) = 198 sq-cm
Hence, (1/2*b*h) = 198/0.99 = 200 sq-cm

Total surface area of solid hemisphere =$3\pi r^2 = 3\frac{22}{7}*7*7$ = 462

Since Angle XEA and XFC are corresponding angles,
Angle XEA = Angle XFC = 100 degrees
Angle XFC + Angle XFD = 180 degrees
Angle XFD = 180-100 = 80 degrees

Since the sum of exterior angles on the same side of the transversal is equal to 180 degrees,

Angle XEB + Angle DFY = 180 degrees

110 + Angle DFY = 180

Angle DFY = 180-110 = 70 degrees

Consider the hexagon ABCDEF as shown.Join BF, CF and CE.

The hexagon is divided into 4 triangles.

Sum of angles of hexagon = 180*4 = 720 degrees.

Since the sum of the exterior angles of the triangles is 360 degrees,
Exterior Angle to A = 360-(120+150) = 90 degrees.

Area of circle = $\pi r^2$ and circumference is $2 \pi r$.
Thus, the ratio is $\frac{r}{2}$
Now, the side of the square will be equal to the diameter of the circle.

=> Diameter = 2r = 8.
=> r/2 = 2

4.5 x l = 5 x 5
So, l = 25/4.5 = 5.56 metres.

The diagonal of a square is $\sqrt {2}$ times the side. Let us assume that ‘a’ is length of side of the square.

$\sqrt{2}a$ = 52

$\Rightarrow$ a = $26\sqrt{2}$

So, area = $a ^{2}$ = $(26\sqrt{2})^{2}$ = 1352 (Answer :C)

The perimeter of the square = 20. So, the side is 20/4 = 5 metres. The circumference of the circle is 2 x $\pi$ x r = 2 x 3.14 x 2.5 = 15.70

circumference of circle = 2πR = 35.2

R is the radius if circle

R= 5.6 cm

Area of circle = π$(R)^2$ = 3.14 × $(5.6)^2$ = 98.56 sq cm

The area of rectangle = l x b = l x $\frac {l}{3} = \frac{l^{2}}{3}$
The area of square = $l ^ {2}$
So, the req. ratio = $l ^ {2}$ : $\frac{l^{2}}{3}$ = 3:1