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 Volume and Surface Area Questions

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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 2141
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 2135
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 2132
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 2110
Q:

Sum of lengths of all edges of a cube is 84 cm, find its volume?

A) 686 cubic cms B) 343 cubic cms
C) 171.5 cubic cms D) 514.5 cubic cms
 
Answer & Explanation Answer: B) 343 cubic cms

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1 2094
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 2085
Q:

The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.
What is the surface area of the cuboid?

A) 288 sq.cm B) 216 sq.cm
C) 144 sq.cm D) Cannot be determined due to insufficient data
 
Answer & Explanation Answer: A) 288 sq.cm

Explanation:
Let lengths, breadth and height of cuboid be l, b and h respectively
According to question
l+b+h = 22cm......(i)
and
√(l^2+b^2+h^2) = 14cm .....(ii)
Surface area of cuboid = 2(lb+bh+lh)
Squaring eq (i) gives
l2+b2+h2+ 2(lb+bh+lh) = 484
Substituting l^2+b^2+h^2 from eq (i)
2(lb+bh+lh) = 484 -196 = 288 sq.cm
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0 2083
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 2068