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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:

Water flows into a tank 200 m x 160 m through a rectangular pipe of 1.5m x 1.25 m @ 20 kmph . In what time (in minutes) will the water rise by 2 meters?

A) 92min B) 93min
C) 95min D) 96min
 
Answer & Explanation Answer: D) 96min

Explanation:

Volume required in the tank = (200 x 150 x 2) cu.m = 60000 cu.m 

Length of water column flown in1 min =(20 x 1000)/60 m =1000/3 m 

Volume flown per minute = 1.5 x 1.25 x (1000/3) cu.m= 625 cu.m. 

Required time = (60000/625)min = 96min

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12 12230
Q:

There is a cylinder circumscribing the hemisphere such that their bases are common. Find the ratio of their volumes

A) 3/2 B) 5/2
C) 7/2 D) 9/2
 
Answer & Explanation Answer: A) 3/2

Explanation:

R =OA = OB = Radius of hemisphere.
= Radius of cylinder ABCD.
Height of the cylinder = BC = radius

 

Volume of cylinder/Volume of hemisphere = πr323πr3

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16 11801
Q:

The height of the wall is 6 times its width and lenght of the wall is 7 times its height .if the volume of the wall be 16128 cu.m.its width is

A) 4m B) 5m
C) 6m D) 7m
 
Answer & Explanation Answer: A) 4m

Explanation:

Let width = x

Then, height = 6x and length = 42x 

42x * 6x * x = 16128

x = 4

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12 11483
Q:

If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in sq.cm) is ?

A) 100 π B) 101/π
C) 99 π/12 D) 54/13π
 
Answer & Explanation Answer: A) 100 π

Explanation:

4/3 π x 10 x 10 x 10 = 8 x 4/3 π x r x r x r
r = 5
4π x 5 x 5 = 100π

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17 10691
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 10688
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 10677
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 10392
Q:

The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles  ?

A) 2413 sq.m B) 1234 sq.m
C) 4312 sq.m D) 2143 sq.m
 
Answer & Explanation Answer: C) 4312 sq.m

Explanation:

Let the radii of the smaller and the larger circles be 's' m and 'l' m respectively.  

 2πs = 264 and 2πl = 352  

 

 s = 2642π and l = 3522π   

Difference between the areas =πl2-πs2   

  = π1762π2-1322π2 

  = 1762π-1322π  

  = (176 - 132)(176 + 132) / π  

  = (44 x 308) / (22/7) = 4312 sq.m

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18 9985