Volume and Surface Area Questions

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:

∆DEF is right angled at E. If m∠F = 45°, then find the value of (tanD - √3/2).

 

A) -√3/2 B) -1/2√3
C) (2-√3)/2 D) (3√3-1)/3
 
Answer & Explanation Answer: C) (2-√3)/2

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

0 16403
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
Exam Prep: Bank Exams
Job Role: Bank PO

45 16328
Q:

Find the total surface area (in cm2) of a right circular cylinder of diameter 7 cm and height 6 cm.

 

A) 187   B) 209  
C) 163   D) 149
 
Answer & Explanation Answer: B) 209  

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

0 16231
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
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

19 15945
Q:

The volume of a hemisphere is 2425.5 cm³. Find its diameter (in cm).

 

A) 10.5   B) 42
C) 21 D) 31.5
 
Answer & Explanation Answer: C) 21

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

0 15925
Q:

Find the total surface area (in cm2) of a hemisphere of diameter 21 cm.

 

A) 1039.5   B) 844.5  
C) 637   D) 472
 
Answer & Explanation Answer: A) 1039.5  

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

2 15752
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

6 15729
Q:

Find the volume (in cm3) of a hemisphere of diameter 7 cm.

 

A) 77   B) 63  
C) 89.83   D) 54.13
 
Answer & Explanation Answer: C) 89.83  

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

0 15693