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:

Which of the following option is CORRECT for SAS similarly criterion for the triangle ABC and DEF?

 

 

A) B)
C) D) All options are correct
 
Answer & Explanation Answer: D) All options are correct

Explanation:
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0 20928
Q:

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

A) 2 : 1 B) 3 : 2
C) 25 : 18 D) 27 : 20
 
Answer & Explanation Answer: C) 25 : 18

Explanation:

Volume of the large cube = 33+43+53 = 216 cu.cm. 

Let the edge of the large cube be a. 

So, a3= 216 

=>a = 6 cm. 

Required ratio = 632+42+52662=2518

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18 20319
Q:

The dimensions of an open box are 50 cm, 40 cm and 23 cm. Its thickness is 2 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box.

A) 8.04kg B) 8.14kg
C) 8.24kg D) 9.04kg
 
Answer & Explanation Answer: A) 8.04kg

Explanation:

Volume of the metal used in the box = External Volume - Internal Volume 

                                                    = [(50 x 40 x 23) - (44 x 34 x 20)] cu.cm  

                                                    = 16080 cu.cm 

 

Weight of the metal =[(16080 x 0.5)/1000] kg = 8.04 kg.

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46 20284
Q:

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

 

A) 140.25 B) 179.67
C) 337.16 D) 213.74
 
Answer & Explanation Answer: B) 179.67

Explanation:
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2 19993
Q:

The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size? 

A) 6 B) 8
C) 12 D) 16
 
Answer & Explanation Answer: B) 8

Explanation:

Side of smallest cube = L.C.M of 5, 10, 20 = 20cm  

Volume of the cube = (20 x 20 x 20)cu.cm = 8000 cu.cm  

Volume of the block= (5 x 10 x 20)cu.cm = 1000 cu.cm  

Number of blocks = (8000/1000) = 8

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35 19008
Q:

Choose the correct option for the figure shown below.

 

A) ∡AOP =∡AOQ B) ∡OAP = ∡OQA
C) AO=OQ D) AP=AO
 
Answer & Explanation Answer: A) ∡AOP =∡AOQ

Explanation:
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0 18813
Q:

Consider the following statements:

1) The number of circles that can be drawn through three non-collinear points is infinity.

2) Angle formed in minor segment of a circle is acute.

Which of the above statements is/are correct?

A) 1 only B) 2 only
C) Both 1 and 2 D) Neither 1 nor 2
 
Answer & Explanation Answer: D) Neither 1 nor 2

Explanation:
(1)
Only one circle can be drawn through 3 non collinear points 
Angle in the minor segment is always obtuse
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1 18479
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:
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2 18077