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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:

66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

A) 84 B) 90
C) 168 D) 336
 
Answer & Explanation Answer: A) 84

Explanation:

Let the length of the wire be h. 

Radius  r =1/2 mm = 1/20 cm  

πr2h = 66  

=> h= (66 x 20 x 20) x (7/22) = 8400cm = 84m 

 

 

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5 10078
Q:

Consider the following inequalities in respect of any triangle ABC:

1) AC –AB < BC

2) BC –AC < AB

3) AB –BC < AC

Which of the above are correct?

A) 1 and 2 only B) 2 and 2 only
C) 1 and 3 only D) 1, 2 and 3
 
Answer & Explanation Answer: D) 1, 2 and 3

Explanation:

AC-AB<BC Or AB+BC>AC

BC-AC<AB Or AB+AC>BC

AB-BC<AC Or AC+BC>AB

Sum of 2 sides of triangle is always greater than the third side

So all three statements are true

 

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1 9817
Q:

A cylindrical rod of iron, whose height is equal to its radius, is melted and cast into spherical balls whose radius is half the radius of the rod. Find the number of balls.

A) 3 B) 4
C) 5 D) 6
 
Answer & Explanation Answer: D) 6

Explanation:

Volume of rod = πr2h = πr2×r = πr3  

Volume of one spherical ball =r/2 

Volume of the spherical ball = 43πr38  

Number of balls=Volumeof rod/volumeof one ball

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15 9728
Q:

Find the surface area (in cm2) of a sphere of diameter 28 cm.

 

A) 3422   B) 3852  
C) 2464   D) 3550
 
Answer & Explanation Answer: C) 2464  

Explanation:
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3 9688
Q:

If radius and height of a cylinder increase by 20% and15% respectively. then what is the % change in curved surface area?

A) 41% B) 38%
C) 33% D) 44%
 
Answer & Explanation Answer: B) 38%

Explanation:

% Change in Curved Surface Area is given by 

%Change in radius + %Change in height + %Change in radius × %Change in height 100  

⇒+20 + 15 + 20×15100 = 38%

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20 9180
Q:

Consider the following statements:

1) An isosceles trapezium is always cyclic.

2) Any cyclic parallelogram is a rectangle.

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:

Since it is an isosceles trapezium

So angle C = angle D = x

let A = 180 –D = 180 –x (since AB is parallel to CD)

B = 180-x

A+C = 180 –x + x = 180 degrees (Property of cyclic quadrilateral)

ABCD is cyclic parallelogram with AB // CD and AD // BC

Considering angles A = C = y (Property of parallelogram) and B=D = x Also since it is cyclic A+C = B+D = 180 degrees

So x=y=90 degrees And also opposite sides are equal being a parallelogram

Thus ABCD is a rectangle

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0 8716
Q:

A cuboid of dimension 24cm x 9cm x 8 cm is melted and smaller cubers are of side 3 cm is formed.find how many such cubes can be formed ?

A) 64 B) 56
C) 48 D) 40
 
Answer & Explanation Answer: A) 64

Explanation:

Volume of cuboid = (24 x 9 x 8) cm = 1728 cu.cm
Volume of small cube = (3 x 3 x 3) cm = 27 cu.cm


So, No. of small cubes formed = 1728/27 = 64.

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5 8358
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 8126