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:

The base of a pyramid is a rectangle whose length and breadth are 16 cm and 12 cm respectively. If the length of all the lateral edges passing through the vertex of the right rectangular pyramid is 26 cm, then find the volume of the pyramid in cubic centimeter?

A) 1536 B) 1024
C) 718 D) 2072
 
Answer & Explanation Answer: A) 1536

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Volume and Surface Area
Exam Prep: CAT , Bank Exams , AIEEE

10 1270
Q:

Two spheres of equal radius are taken out by cutting from a solid cube of side (12 + 4√3) cm. What is the maximum volume (in cm3) of each sphere?

A) 1077.31 B) 905.14
C) 966.07 D) 1007.24
 
Answer & Explanation Answer: B) 905.14

Explanation:
Report Error

View Answer Report Error Discuss

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

1 1268
Q:

The height of a cone is 45 cm. It is cut at a height of 15 cm from its base by a plane parallel to its base. If the volume of the smaller cone is 18480 cm3, then what is the volume (in cm3) of the original cone?

A) 34650 B) 61600
C) 36960 D) 62370
 
Answer & Explanation Answer: D) 62370

Explanation:
Report Error

View Answer Report Error Discuss

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

1 1247
Q:

A cuboid has dimensions 8 cm x 10 cm x 12 cm. It is cut into small cubes of side 2 cm. What is the percentage increase in the total surface area?

A) 286.2 B) 314.32
C) 250.64 D) 386.5
 
Answer & Explanation Answer: D) 386.5

Explanation:
Report Error

View Answer Report Error Discuss

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

1 1237
Q:

The volume of a spherical balloon is increased by 700%. What is the percentage increase in its surface area?

A) 300% B) 400%
C) 450% D) 500%
 
Answer & Explanation Answer: A) 300%

Explanation:
Report Error

View Answer Report Error Discuss

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

4 1235
Q:

A rectangular red carpet of size 6 ft ×12 ft has a dark red border 6 inches wide. What is the area of the dark red border?

 

A) 9 square feet B) 15 square feet
C) 17 square feet D) 18 square feet
 
Answer & Explanation Answer: C) 17 square feet

Explanation:
Initially carpet is 6×12 = 72 sq feet
Since red border is 6 inches wide from all 4 side
So area without border = 5× 11 = 55 sq feet
Area of border = total–area without border = 72–55 = 17 sq feet
Report Error

View Answer Report Error Discuss

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

0 1232
Q:

The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.
If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?

A) 572 cub.cm B) 728 cub.cm
C) 1144 cub.cm D) None of the above
 
Answer & Explanation Answer: C) 1144 cub.cm

Explanation:
Report Error

View Answer Report Error Discuss

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

2 1205
Q:

A solid cube has side 8 cm. It is cut along diagonals of top face to get 4 equal parts. What is the total surface area (in cm2) of each part?

A) 96 + 64√2 B) 80 + 64√2
C) 96 + 48√2 D) 80 + 48√2
 
Answer & Explanation Answer: A) 96 + 64√2

Explanation:
Report Error

View Answer Report Error Discuss

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

2 1197