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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:

From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of remaining solid?

A) 272 cub.cm B) 270 cub.cm
C) 300 cub.cm D) 277 cub.cm
 
Answer & Explanation Answer: D) 277 cub.cm

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3 853
Q:

An inverted conical shaped vessel is filled with water to its brim. The height of the vessel is 8 cm and radius of the open end is 5 cm . When a few solid spherical metallic balls each of radius 1⁄2 cm are dropped in the vessel , 25% water is overflowed. The number of balls is:

A) 100 B) 400
C) 200 D) 150
 
Answer & Explanation Answer: A) 100

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Q:

What is the curved surface area (in cm²) of a hemisphere of diameter 42 cm?

A) 2332 B) 1778
C) 1556 D) 2772
 
Answer & Explanation Answer: D) 2772

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0 851
Q:

In a triangle ABC, if ∡A +∡C = 140° and ∡A + 3∡B = 180°, then ∡A is equal to

A) 80° B) 40°
C) 60° D) 20°
 
Answer & Explanation Answer: C) 60°

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0 850
Q:

A tent is to be built in the form of a cylinder of radius 5 m surmounted by a cone of the same radius. If the height of the cylindrical part is 6 m and slant height of the conical part is 10 m, how much canvas will be required to build the tent? Allow 20% extra canvas for folding and stitching. (Take π = 22/7)

A) 829.72 sq mts B) 414.86 sq mts
C) 1244.58 sq mts D) 207.43 sq mts
 
Answer & Explanation Answer: B) 414.86 sq mts

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0 850
Q:

Suppose that the medians BD, CE and AF of a triangle ABC meet at G. Then AG: GF is

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

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3 849
Q:

ΔPQR is right angled at Q. If cosP = 3/5, then what is the value of cosR ?

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

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1 849
Q:

The area and the length of one of the diagonals of a rhombus is 60 cm2 and 8 cm respectively. Find the length of its other diagonal (in cm).

A) 7.5 B) 30
C) 22.5 D) 15
 
Answer & Explanation Answer: D) 15

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0 846