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:

The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall.

A) 40cm B) 30cm
C) 20cm D) 10cm
 
Answer & Explanation Answer: A) 40cm

Explanation:

Let the breadth of the wall be x metres. 

Then, Height = 5x metres and Length = 40x metres.  

x * 5x * 40x = 12.8   

=>x3 =12.8/200 = 128/2000 =64/1000  

=> x = 4/10 m  

=> x = (4/10)*100 = 40 cm

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52 24988
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 24550
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 24297
Q:

Find the volume (in cm3) of a right circular cone of diameter 7 cm and height 7 cm.

 

A) 69.06   B) 16.43  
C) 11.15   D) 89.83
 
Answer & Explanation Answer: D) 89.83

Explanation:
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0 24241
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 23689
Q:

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:

A) 90 cm B) 1 dm
C) 1 m D) 1.1 cm
 
Answer & Explanation Answer: B) 1 dm

Explanation:

ke

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35 23471
Q:

Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high.

A) 14m B) 15m
C) 16m D) 17m
 
Answer & Explanation Answer: D) 17m

Explanation:

Length of longest pole = Length of the diagonal of the room

 

122+82+92=289 = 17m

 

 

 

 

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35 22788
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:
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