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:

In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

A) 75 cubic meter B) 750 cubic meter
C) 7500 cubic meter D) 75000 cubic meter
 
Answer & Explanation Answer: B) 750 cubic meter

Explanation:

1 hectare = 10,000 Sq.m

So, Area = (1.5 x 10000) Sq.m

Depth = 5/100 m = 1/20 m

Therefore, Volume = Area X Depth = 15000 x (1/20)= 750 cu.m

Report Error

View Answer Report Error Discuss

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

29 12422
Q:

Water flows into a tank 200 m x 160 m through a rectangular pipe of 1.5m x 1.25 m @ 20 kmph . In what time (in minutes) will the water rise by 2 meters?

A) 92min B) 93min
C) 95min D) 96min
 
Answer & Explanation Answer: D) 96min

Explanation:

Volume required in the tank = (200 x 150 x 2) cu.m = 60000 cu.m 

Length of water column flown in1 min =(20 x 1000)/60 m =1000/3 m 

Volume flown per minute = 1.5 x 1.25 x (1000/3) cu.m= 625 cu.m. 

Required time = (60000/625)min = 96min

Report Error

View Answer Report Error Discuss

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

12 11080
Q:

There is a cylinder circumscribing the hemisphere such that their bases are common. Find the ratio of their volumes

A) 3/2 B) 5/2
C) 7/2 D) 9/2
 
Answer & Explanation Answer: A) 3/2

Explanation:

R =OA = OB = Radius of hemisphere.
= Radius of cylinder ABCD.
Height of the cylinder = BC = radius

 

Volume of cylinder/Volume of hemisphere = πr323πr3

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

16 11001
Q:

How many iron rods, each of length 7 mts and diameter 2 cms can be made out of 0.88 cubic metre of iron ?

A) 500 B) 600
C) 400 D) 300
 
Answer & Explanation Answer: C) 400

Explanation:

Given length of iron rod =7 mts and  and diameter of rod = 2 cms 

=> r = 1/100 mts

Therefore,  Volume of one rod = πr2h cu. m =  227×11002×7cu. m = 115000 cu. m

Given volume of iron = 0.88 cu. m 

Therefore, Number of rods = 0.88×500011 = 400.

Report Error

View Answer Report Error Discuss

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

16 10836
Q:

The height of the wall is 6 times its width and lenght of the wall is 7 times its height .if the volume of the wall be 16128 cu.m.its width is

A) 4m B) 5m
C) 6m D) 7m
 
Answer & Explanation Answer: A) 4m

Explanation:

Let width = x

Then, height = 6x and length = 42x 

42x * 6x * x = 16128

x = 4

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

12 10821
Q:

If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in sq.cm) is ?

A) 100 π B) 101/π
C) 99 π/12 D) 54/13π
 
Answer & Explanation Answer: A) 100 π

Explanation:

4/3 π x 10 x 10 x 10 = 8 x 4/3 π x r x r x r
r = 5
4π x 5 x 5 = 100π

Report Error

View Answer Report Error Discuss

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

17 10015
Q:

66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

A) 84 B) 90
C) 168 D) 336
 
Answer & Explanation Answer: A) 84

Explanation:

Let the length of the wire be h. 

Radius  r =1/2 mm = 1/20 cm  

πr2h = 66  

=> h= (66 x 20 x 20) x (7/22) = 8400cm = 84m 

 

 

Report Error

View Answer Report Error Discuss

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

5 9925
Q:

A cylindrical rod of iron, whose height is equal to its radius, is melted and cast into spherical balls whose radius is half the radius of the rod. Find the number of balls.

A) 3 B) 4
C) 5 D) 6
 
Answer & Explanation Answer: D) 6

Explanation:

Volume of rod = πr2h = πr2×r = πr3  

Volume of one spherical ball =r/2 

Volume of the spherical ball = 43πr38  

Number of balls=Volumeof rod/volumeof one ball

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

15 9441