Sawaal

 Volume and Surface Area Questions

Popular Latest Rated Important Formulae

FACTS  AND  FORMULAE  FOR  VOLUME  AND  SURFACE  AREA  QUESTIONS

 

 

I. CUBOID

   Let length=l, breadth =b and height =h units. Then,

1. Volume = (l x b x h)

2. Surface area = 2(lb +bh + lh) sq.units

3. Diagonal =l2+b2+h2 units

 

 

II. CUBE 

Let each edge of a cube be of length a. Then,

1. Volume = a3 cubic units.

2. Surface area = 6a2 sq.units

3. Diagonal = 3a units

 

 

III. CYLINDER 

Let radius of base = r and Height (or Length) = h. Then, 

1.Volume = πr2h cubic units 

2. Curved surface area = 2πrh sq.units

3. Total surface area = 2πrh+2πr2 sq.units

 

 

IV. CONE 

Let radius of base =r and Height = h. Then, 

1. Slant height, l=h2+r2 units

 

2. Volume = 13πr2h cubic units.

 

3. Curved surface area = πrlsq.units 

 

4. Total surface area = πrl+πr2sq.units

 

 

V. SPHERE 

Let the radius of the sphere be r. Then, 

1. Volume =43πr3 cubic units

2. Surface area = 4πr2 sq.units

 

 

VI. HEMISPHERE 

Let the radius of a hemisphere be r. Then, 

1. Volume = 23πr3 cubic units.

2. Curved surface area = 2πr2 sq.units

3. Total surface area = 3πr2 sq.units

 

Q:

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

A) 2 : 1 B) 3 : 2
C) 25 : 18 D) 27 : 20
 
Answer & Explanation Answer: C) 25 : 18

Explanation:

Volume of the large cube = 33+43+53 = 216 cu.cm. 

Let the edge of the large cube be a. 

So, a3= 216 

=>a = 6 cm. 

Required ratio = 632+42+52662=2518

Report Error

View Answer Report Error Discuss

Filed Under: Volume and Surface Area - Quantitative Aptitude - Arithmetic Ability

18 18113
Q:

A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8g/cu.cm, then the weight of the pipe is

A) 3.6 kg B) 3.696 kg
C) 36 kg D) 36.9 kg
 
Answer & Explanation Answer: B) 3.696 kg

Explanation:

External radius = 4 cm 

Internal radius = 3 cm 

Volume of iron = 227×42-32×21cm3= 462cm3   

Weight of iron = (462 x 8)gm = 3696 gm = 3.696 kg

Report Error

View Answer Report Error Discuss

Filed Under: Volume and Surface Area - Quantitative Aptitude - Arithmetic Ability

28 16606
Q:

How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?

A) 5600 B) 6000
C) 6400 D) 7200
 
Answer & Explanation Answer: C) 6400

Explanation:

Number of bricks = volume of the wall/volume of one brick 

= (800 x 600 x 22.5)/(25 x 11.25 x 6 )= 6400

 

 

 

 

Report Error

View Answer Report Error Discuss

Filed Under: Volume and Surface Area - Quantitative Aptitude - Arithmetic Ability

20 15962
Q:

The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size? 

A) 6 B) 8
C) 12 D) 16
 
Answer & Explanation Answer: B) 8

Explanation:

Side of smallest cube = L.C.M of 5, 10, 20 = 20cm  

Volume of the cube = (20 x 20 x 20)cu.cm = 8000 cu.cm  

Volume of the block= (5 x 10 x 20)cu.cm = 1000 cu.cm  

Number of blocks = (8000/1000) = 8

Report Error

View Answer Report Error Discuss

Filed Under: Volume and Surface Area - Quantitative Aptitude - Arithmetic Ability
Exam Prep: Bank Exams
Job Role: Bank PO

35 15770
Q:

How many cubes of 10cm edge can be put in a cubical box of 1m edge

A) 10 B) 100
C) 1000 D) 10000
 
Answer & Explanation Answer: C) 1000

Explanation:

Number of cubes= (100x100x100) / (10x10x10)= 1000

Report Error

View Answer Report Error Discuss

Filed Under: Volume and Surface Area - Quantitative Aptitude - Arithmetic Ability
Exam Prep: Bank Exams
Job Role: Bank PO

45 15627
Q:

A cuboidal block 6cm x 9cm x 12cm is cut up into an exact number of equal cubes.The least possible number of equal cubes will be

A) 6 B) 9
C) 24 D) 30
 
Answer & Explanation Answer: C) 24

Explanation:

Volume of block=(6 x 9 x 12) cu.cm = 648 cu.cm 

Side of largest cube = H.C.F of 6,9,12 = 3cm 

Volume of the cube=(3 x 3 x 3)=27cu.cm 

Number of cubes=(648/27)=24

Report Error

View Answer Report Error Discuss

Filed Under: Volume and Surface Area - Quantitative Aptitude - Arithmetic Ability
Exam Prep: Bank Exams
Job Role: Bank PO

18 15571
Q:

If the volume of the cube is 729 cm3, then the surface area of the cube will be

A) 486 sq.cm B) 456 sq.cm
C) 446 sq.cm D) 476 sq.cm
 
Answer & Explanation Answer: A) 486 sq.cm

Explanation:

volume = a3 = 729;

=> a = 9

 

surface area= 6a2 =  (6 x 9 x 9) = 486 sq.cm

Report Error

View Answer Report Error Discuss

Filed Under: Volume and Surface Area - Quantitative Aptitude - Arithmetic Ability
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

19 14999
Q:

What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?

A) 344.35 sq.cm B) 462 sq.cm
C) 498.35 sq.cm D) None of these
 
Answer & Explanation Answer: C) 498.35 sq.cm

Explanation:

h = 14 cm, r = 7 cm.  

So, l =72+142 = 245 = 75cm   

Total surface area = πrl+πr2 = 227×7×75 + 227×7×7 

=1545+1 

= (3.236 x 154) sq.cm   

= 498.35 sq.cm

Report Error

View Answer Report Error Discuss

Filed Under: Volume and Surface Area - Quantitative Aptitude - Arithmetic Ability

6 14741