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 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 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%

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4 2058
Q:

Identical cubes of largest possible size are cut from a solid cuboid of size 65 cm × 26 cm × 3.9 cm. What is the total surface area (in cm2) of all the small cubes taken together?

A) 30420 B) 15210
C) 20280 D) 16440
 
Answer & Explanation Answer: A) 30420

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5 2051
Q:

Volume of a cylinder is 770 cubic cm. If circumference of its base is 22 cm, what will be the curved surface area of the cylinder? (Take π = 22/7)

A) 440 sq cms B) 880 sq cms
C) 220 sq cms D) 660 sq cms
 
Answer & Explanation Answer: A) 440 sq cms

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1 2037
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

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1 1995
Q:

A right triangular pyramid XYZB is cut from cube as shown in figure. The side of cube is 16 cm. X, Y and Z are mid points of the edges of the cube. What is the total surface area (in sq.cm) of the pyramid?

 

A) 48[(√3) + 1] B) 24[4 + (√3)]
C) 28[6 + (√3)] D) 32[3 + (√3)]
 
Answer & Explanation Answer: D) 32[3 + (√3)]

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2 1987
Q:

A solid sphere has a radius 21 cm. It is melted to form a cube. 20% material is wasted in this process. The cube is melted to form hemisphere. In this process 20% material is wasted. The hemisphere is melted to form two spheres of equal radius. 20% material was also wasted in this process. What is the radius (in cm) of each new sphere?

A) 4.2 (23) B) 2.1 23
C) 2.1 43 D) 4.2 43
 
Answer & Explanation Answer: B) 2.1 23

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0 1986
Q:

In the given figure, in triangle STU, ST = 8 cm,TU = 9 cm and SU = 12 cm. QU = 24 cm, SR = 32 cm and PT = 27 cm. What is the ratio of the area of triangle PQU and area of triangle PTR?

A) 1 : 1 B) 1 : 4
C) 2 : 3 D) Unknown
 
Answer & Explanation Answer: D) Unknown

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0 1973
Q:

In the given figure, radius of a circle is 14√2 cm. PQRS is a square. EFGH, ABCD, WXYZ and LMNO are 4 identical squares. What is the total area (in sq.cm) of all the small squares ?

A) 31.36 B) 125.44
C) 62.72 D) 156.8
 
Answer & Explanation Answer: A) 31.36

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0 1969