RRB NTPC - Problems on Volumes

1.

The radius of the cylinder and cone are equal. find its volumes ratio: 

   A.) 1 : 3
   B.) 3 : 1
   C.) 2 : 1
   D.) 3 : 2

Answer: Option 'B'

radius of the cylinder = radius of the cone 
πr2h = 1/3 πr2h 1 : 1/3 
3 : 1

2.

The diagonal of a cube is 8√3. find its volume and surface area. 

   A.) 34 Cm2
   B.) 364 Cm3
   C.) 384 Cm2
   D.) 384 Cm3

Answer: Option 'D'

√3.a = 8 √3 => a = 8 
Volume = a3 => (8 × 8 × 8) Cm3 => 512 Cm3
Surface area => 6 a2 => (6 × 8 × 8) Cm2 => 384 Cm2

3.

Find the volume of cuboid 15 m length, 9 m breadth and 2 m height. 

   A.) 1420 m3
   B.) 1440 m2
   C.) 1424 m3
   D.) 1440 m3

Answer: Option 'D'

Cuboid volume => l × b × h => 15 × 12 × 8 = 1440 m3

4.

If the radius of the sphere is 14 m. then its total surface area is: 

   A.) 2464
   B.) 2364
   C.) 2465
   D.) 2461

Answer: Option 'A'

Sphere Total surface area = 4πr2 = 4 × 22/7 × 14 × 14 = 2464

5.

The length of box 12 Cm long, 8 Cm breadth and 9Cm height. Find the length of pencil in that box?

   A.) 17 Cm2
   B.) 18 Cm
   C.) 17 Cm
   D.) 18 Cm3

Answer: Option 'C'

Diagonal (d) = √l2+b2+h2 
= √122+82+92 
= √144+64+81 
= √289 => 17 Cm

6.

If each edge of cube increased by 10%, the percentage increase in surface area is: 

   A.) 33.1%
   B.) 33%
   C.) 32.2
   D.) 32.3

Answer: Option 'A'

100 × (110)/100 × (110)/100 × (110)/100 => 1331/100 = 33.1%

7.

A cylinder and a cone have the same height and same radius of base. The ratio between the volumes of the cylinder and the cone is:

   A.) 3 : 1
   B.) 3 : 2
   C.) 2 : 1
   D.) None of these

Answer: Option 'A'

Volume of the cylinder = πr2
Volume of the cone = 1/3 πr2
(πr2h)/(1/3 πr2h) = 3/1 = 3 : 1

8.

The radius of hemi-sphere is 7 m. Find it's total surface area?

   A.) 452 m3
   B.) 462 m2
   C.) 462 m3
   D.) None of these

Answer: Option 'C'

otace area = 3πr2 sq.units 
= 3 × 22/7 × 7 × 7 
= 66 × 7 = 462 m3

9.

How many box's of length 40 Cm, width 30 Cm and height 10 Cm can be formed from a box of 6 m length, 4 m width and 2 m height.

   A.) 400
   B.) 3500
   C.) 4000
   D.) 2000

Answer: Option 'C'

(600×400×200)/(40×30×10) = 4000

10.

The radius of a cylinder is 6 m, height 21 m. The total surface area of the cylinder is? 

   A.) 528 Cm3
   B.) 538 Cm3
   C.) 527 Cm3
   D.) 528 Cm2

Answer: Option 'D'

Total surface area of the cylinder is = 2πr (r+h) 
= 2 × 22/7 × 6(6+8) 
= 2 × 22/7 × 6(14) = 44 × 12 = 528 m2

11.

The radius of hemi sphere 7 m, find its volume? 

   A.) 205 1/4 m3 cubic units
   B.) 205 1/3 m3 cubic units
   C.) 205 1/3 m2 cubic units
   D.) None of these

Answer: Option ''

Hemi-sphere volume (V) = 2/3 πr3 
= 2/3 × 22/7 × 7 × 7 × 7 
= (44 × 49)/3 = 616/3 = 205 1/3 m3 cubic units

12.

If each edge of cube increased by 20%, the percentage increase in 

   A.) 44%
   B.) 34%
   C.) 48%
   D.) 42%

Answer: Option 'A'

100 × (120)/100 × (120)/100 = 144 => 44%

13.

The lateeral surface area of cuboid length 12 m, breadth 8 m and height 6m

   A.) 230 m3
   B.) 240 m3
   C.) 230 m2
   D.) 240 m2

Answer: Option 'D'

Cuboid lateral surface = 2h(l+b) 
= 2 × 6 (20) = 240 m2

14.

The volume of cube is equal to the surface area of that cube. Then find the distance of side of the cube?

   A.) 6 m
   B.) 7 m
   C.) 8 m
   D.) 9 m

Answer: Option 'A'

Cube volume = a3 cubic units 
Surface area = 6 a2 sq.units 
a3 = 6 a2
a = 6 m

15.

The side of a cube is 8 m, Find the voiume? 

   A.) 513 m3
   B.) 514 m3
   C.) 512 m3
   D.) 502 m3

Answer: Option 'C'

Cube Volume = a3
a3 = 83 = 512 m3

16.

The height of a cylinder is 60 Cm and the diameter of its base is 5 Cm. The total surface area of the cylinder is : 

   A.) 981 Cm2
   B.) 982.13 Cm2
   C.) 982.14 Cm2
   D.) None of these

Answer: Option 'C'

Given h = 60 Cm and r = 5/2 Cm 
Total surface area = 2πrh + 2&pir2 
= 2πr(h+r) 
= [2 × 22/7 × 5/2 × (60 + 5/2)] Cm2 
= [ 44/7 × 5/2 × ( (120 + 5)/2 ) ] Cm2 
= 22/7 × 5 × 125/2 Cm2 
= (55 × 125)/7 Cm2 
= 6875/7 Cm2 
= 982.14 Cm2

17.

The radius of a cylinder is 10 m, height 14 m. The volume of the cylinder is: 

   A.) 4000 m2
   B.) 4300 m2
   C.) 4000 m3
   D.) None of these

Answer: Option 'C'

Cylinder volume = πr2h
= 22/7 × 10 × 10 × 14 
= 4400 m3

18.

The side of a cube is 15 m, find it's surface area? 

   A.) 1350 m2
   B.) 1250 m2
   C.) 1300 m2
   D.) 1450 m2

Answer: Option 'A'

Surface area = 6 a2 sq. units
6 a2 = 6 × 225 = 1350 m2

19.

The radius of a cone is 8 m, height 6 m. Find the slant height? 

   A.) 10 Cm
   B.) 15 Cm
   C.) 10 m
   D.) 15 m

Answer: Option 'B'

Answer: Option 'B'
Cone slant height (l) = √r2+h2 
= √64+36 = 10 m.

20.

The height of cylinder is 14 Cm and its diameter is 10 Cm. The volume of the cylinder is:

   A.) 110 Cm3
   B.) 1100 Cm3
   C.) 1101 Cm2
   D.) 1101 Cm3

Answer: Option 'B'

h = 14 Cm and r = 5 Cm 
Cylinder volume = πr2h = (22/7 × 5 × 5 × 14) Cm3 = 1100 Cm3


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