Volume questions for Railways PDF

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Volume questions for Railways PDF
Volume questions for Railways PDF

Volume questions for Railways PDF

Download Top-15 RRB Group-D Volume questions and answers PDF. RRB Group – D Volume questions and answers based on asked questions in previous exam papers very important for the Railway Group-D exam.

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Question 1: The total surface area of a sphere is 8π square unit. The volume of the sphere is

a) 83π

b) 83π

c) 835π

d) 823π

Question 2: The perimeter of one face of a cube is 20 cm. Its volume will be

a) 625 cm

b) 100 cm

c) 125 cm

d) 400 cm

Question 3: If the volume of a sphere is numerically equal to its surface area then its diameter is

a) 6cm

b) 4 cm

c) 2 cm

d) 3 cm

Question 4: The base of a right prism is a quadrilateral ABCD. Given that AB = 9 cm, BC = 14 cm, CD = 13 cm, DA = 12 cm and ΔDAB = 90°. If the volume of the prism be 2070 cm3, then the area of the lateral surface is

a) 720 cm2

b) 810 cm2

c) 1260 cm2

d) 2070 cm2

Question 5: The volumes of a right circular cylinder and a sphere are equal. The radius of the cylinder and the diameter of the sphere are equal. The ratio of height and radius of the cylinder is

a) 3 : 1

b) 1 : 3

c) 6 : 1

d) 1 : 6

Question 6: The perimeter of the base of a right circular cylinder is ‘a’ unit. If the volume of the cylinder is V cubic unit, then the height of the cylinder is

a) 4a2vπ

b) 4πa2v

c) πa2vv

d) 4πva2

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Question 7: The curved surface area and the total surface area of a cylinder are in the ratio 1:2 If the total surface area of the right cylinder is 616 cm , then its volume is :

a) 1232Cm3

b) 1848Cm3

c) 1632Cm3

d) 1078Cm3

Question 8: The perimeter of the base of a right circular cone is 8 cm. If the height of the cone is 21 cm, then its volume is:

a) 108πcm3

b) 112πcm3

c) 112πcm3

d) 108πcm3

Question 9: The radius of the base and the height of a right circular cone are doubled. The volume of the cone will be

a) 8 times of the previous volume

b) three times of the previous volume

c)  3√2 times of the previous volume

d) 6 times of the previous volume

Question 10: If the ratio of volumes of two cones is 2 : 3 and the ratio of the radii of their bases is 1 : 2, then the ratio of their heights will be

a) 8 : 3

b) 3 : 8

c) 4 : 3

d) 3 : 4

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Question 11: The diameter of a garden roller is 1.4 metre and it is 2 metre long. The area covered by the roller in 5 revolutions is :

a) 8.8 sq.m

b) 4.4 sq.m

c) 44 sq.m

d) 16.8 sq.m

Question 12: A bicycle wheel makes 5000 revolutions in moving 11km.Then the radius of the wheel (in cm) is

a) 70

b) 35

c) 17.5

d) 140

Question 13: If the radius of the cylinder and of a sphere having the same volume as that cylinder is ‘r’ then what is the height of that cylinder?

a) 3/2 r

b) 2/3 r

c) 4/3 r

d) 3/4 r

Question 14: Volume of a cylinder is 2310 cubic cm. If circumference of its base is 44 cm, find the curved surface area of the cylinder?

a) 660 sq cm

b) 1320 sq cm

c) 1980 sq cm

d) 330 sq cm

Question 15: If the curved surface area of a right circular cone is 10010 sq cm and its radius is 35 cm, find its volume?

a) 6930 cubic cm

b) 107800 cubic cm

c) 3465 cubic cm

d) 27720 cubic cm

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Answers & Solutions:

1) Answer (D)

Let the radius of the sphere be ‘r’
Hence 4πr2 = 8π
=> r = 2
Volume of the cube = 43πr3 = 43π23 = 823π

2) Answer (C)

Let each side of the cube be a

One face of a cube is a square with perimeter 20 cm

=> 4 * a = 20

=> a = 5

Volume of cube = a3

= 53 = 125 cm3

3) Answer (A)

Let the radius of sphere = r

Since, volume of sphere = surface area

=> 43πr3=4πr2

=> r=3

=> Diameter = 2 * r = 2*3 = 6 cm

4) Answer (A)

In right DAB, using Pythagoras theorem,

=> BD=(AD)2+(AB)2

=> BD=122+92=225

=> BD=15cm

Now, area of DAB = 12912=54cm2

Area of BCD = s(sa)(sb)(sc)

where, s=a+b+c2

=> Area of BCD = 21678=84cm2

=> Area of quad ABCD = area of DAB + area of BCD

= 54+84 = 138cm2

Volume of prism = base area * height

=> 2070 = 138 * height

=> height = 15 cm

Lateral surface area of prism = perimeter of base * height

= (12 + 9 + 14 + 13) * 15 = 48 * 15

= 720 cm2

5) Answer (D)

Let the radius and height of right circular cylinder be r and h respectively.

Let radius of sphere is R.

The radius of the cylinder and the diameter of the sphere are equal.

Therefore, r = 2R

The volumes of a right circular cylinder and a sphere are equal.

=> πr2h=43πR3

=> 3r2h=4(r2)3

=> 6r2h=r3

=> 6h=r

=> hr=16

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6) Answer (D)

Perimeter of base = 2πr=a

=> r=a2π

Volume of cylinder = πr2h=V

=> π(a2π)2h=V

=> a2h=4πV

=> h=4πVa2

7) Answer (D)

Let radius of cylinder be r and height be h

=> 2πrh2πrh+2πr2=12

=> hh+r=12

=> h=r

Total surface area = 2πrh+2πr2=616

=> 2πr2+2πr2=616

=> r2=154722

=> r=7=h

Now, volume of cylinder = πr2h

= 227727

= 1078cm3

8) Answer (B)

Let the radius of the cone be r and height = 21

=> Perimeter of base = 2πr=8

=> r=4π

Volume of cone = 13πr2h

= 13π(4π)221

= 112πcm3

9) Answer (A)

Let original radius be r and height be h

=> Original volume of cone = 13πr2h

New radius = 2r and new height = 2h

=> New volume = 13π(4r2)(2h)

= 813πr2h

=> New volume of cone = 8 times the previous one.

10) Answer (A)

Let the radii of two cones be r1=x and r2=2x

Let the heights of the two cones be h1 and h2

=> Ratio of volumes :

=> 13πr12h113πr22h2=23

=> x2h14x2h2=23

=> h1h2=83

=> Required ratio = 8 : 3

11) Answer (C)

We know that, Surface area of cylinder = π × d × L Where, d and L are diameter and length of the cylinder
Given, Diameter of the roller = 1.4 m & Length of the roller = 2 m

∴ Surface area of the roller = π × 1.4 × 2 = (22/7) × 1.4 × 2 = 8.8 m2
∴ Area covered by 5 revolution = 5 × 8.8 m2 = 44 m2

12) Answer (B)

The distance of 11km is covered by the perimeter of tyre by 5000 revolutions.
Hence, 11×1000×100=5000× πD
D = 70cm
r = 35cm

13) Answer (C)

volume of sphere = 43 πr3

volume of cylinder = πr2h

given that radius and volume of both are same

so  43 πr3πr2h

43r  =  h

so the answer is option C.

14) Answer (A)

Let radius of base of cylinder = r cm and height = h cm

Circumference of base = 2πr=44

=> 2×227×r=44

=> r=44×744=7 cm

Now, volume of cylinder = πr2h=2310

=> 227×(7)2×h=2310

=> 22×7×h=2310

=> h=2310154=15 cm

Curved Surface area of cylinder = 2πrh

= 44×15=660cm2

15) Answer (B)

Let slant height of cone = l cm and radius = 35 cm

Curved surface area of cone = πrl=10010

=> 227×35×l=10010

=> 22×5×l=10010

=> l=10010110=91

Let height of cone = h cm

=> (h)2=(l)2(r)2

=> (h)2=(91)2(35)2

=> (h)2=82811225=7056

=> h=7056=84

Volume of cone = 13×πr2h

= 13×227×(35)2×84

= 22×(35)2×4=107800cm3

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We hope this Volume questions  and answers PDF for RRB Group-D Exam will be highly useful for your preparation.

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