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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:

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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0 18180
Q:

In the figure ∠AMB = 130°, then what is the value (in deg) of ∠ABQ?

 

A) 40 B) 50
C) 60 D) 90
 
Answer & Explanation Answer: B) 50

Explanation:
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3 17777
Q:

Consider the following statements:

1) The perimeter of a triangle is greater than the sum of its three medinas.

2) In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD.

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: C) Both 1 and 2

Explanation:
Let ABC be the triangle and D. E and F are midpoints of BC, CA and AB respectively.
Recall that the sum of two sides of a triangle is greater than twice the median bisecting the third side,(Theorem to be remembered)
Hence in ΔABD, AD is a median
⇒
AB + AC > 2(AD)
Similarly, we get
BC + AC > 2CF
BC + AB > 2BE
On adding the above inequations, we get
(AB + AC) + (BC + AC) + (BC + AB )> 2AD + 2CD + 2BE
2(AB + BC + AC) > 2(AD + BE + CF)
∴
AB + BC + AC > AD + BE +CF
 
2.
To prove: AB + BC + CA > 2AD
Construction: AD is joined
Proof: In triangle ABD,
AB + BD > AD [because, the sum of any two sides of a triangle is always greater than the
third side]
----
1
In triangle ADC,
AC + DC > AD [because, the sum of any two
sides of a tri
angle is always greater than the
third side]
----
2
Adding 1 and 2 we get,
AB + BD + AC + DC > AD + AD
=> AB + (BD + DC) + AC > 2AD
=> AB + BC + AC > 2AD
Hence proved
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1 17411
Q:

A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8g/cu.cm, then the weight of the pipe is

A) 3.6 kg B) 3.696 kg
C) 36 kg D) 36.9 kg
 
Answer & Explanation Answer: B) 3.696 kg

Explanation:

External radius = 4 cm 

Internal radius = 3 cm 

Volume of iron = 227×42-32×21cm3= 462cm3   

Weight of iron = (462 x 8)gm = 3696 gm = 3.696 kg

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28 17405
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 17072
Q:

How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?

A) 5600 B) 6000
C) 6400 D) 7200
 
Answer & Explanation Answer: C) 6400

Explanation:

Number of bricks = volume of the wall/volume of one brick 

= (800 x 600 x 22.5)/(25 x 11.25 x 6 )= 6400

 

 

 

 

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20 16706
Q:

A cuboidal block 6cm x 9cm x 12cm is cut up into an exact number of equal cubes.The least possible number of equal cubes will be

A) 6 B) 9
C) 24 D) 30
 
Answer & Explanation Answer: C) 24

Explanation:

Volume of block=(6 x 9 x 12) cu.cm = 648 cu.cm 

Side of largest cube = H.C.F of 6,9,12 = 3cm 

Volume of the cube=(3 x 3 x 3)=27cu.cm 

Number of cubes=(648/27)=24

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18 16642
Q:

Find the volume (in cub.cm) of a hemisphere of diameter 28 cm.

 

A) 4789.67   B) 3675  
C) 2732 D) 5749.33
 
Answer & Explanation Answer: D) 5749.33

Explanation:
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