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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:

If the diameter of a circle is 35 cm, then what will be its circumference (in cm)?

A) 110 B) 220
C) 21 D) 42
 
Answer & Explanation Answer: A) 110

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Q:

A prism has a regular hexagonal base with side 6 cm. If the total surface area of prism is 216√3 cm2, then what is the height (in cm) of prism?

A) 3√3 B)  6√3
C) 6 D) 3
 
Answer & Explanation Answer: A) 3√3

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Q:

A solid right circular cone of radius 10 cm and height 8 cm is put inside a cylindrical vessel of radius 11 cm and height 9 cm. How much water in cubic cm will be required to fill the cylindrical vessel completely?

A) 5168.96 cubic cms B) 2584.48 cubic cms
C) 7753.44 cubic cms D) 1292.24 cubic cms
 
Answer & Explanation Answer: B) 2584.48 cubic cms

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Q:

The external and the internal radii of a hollow right circular cylinder of height 15 cm are 6.75 cm and 5.25 cm respectively. If it is melted to form a solid cylinder of height half of the orignal cylinder, then the radius of the solid cylinder is

A) 6 cm B) 7.25 cm
C) 6.5 cm D) 7 cm
 
Answer & Explanation Answer: A) 6 cm

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Q:

Which of the following condition is sufficient to state that triangle ABC and DEF are similar?

A) 1 B) 2
C) 3 D) 4
 
Answer & Explanation Answer: A) 1

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Q:

The midpoints of AB and AC of a triangle ABC are X and Y respectively. If BC+XY=12 units, then BC­XY is

A) 10 units B) 8 units
C) 6 units D) 4 units
 
Answer & Explanation Answer: D) 4 units

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Q:

If an interior of a regular polygon is 170o, then the number of sides of the polygon is

A) 30 B) 20
C) 18 D) 27
 
Answer & Explanation Answer: A) 30

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Q:

Δ XYZ is right angled at Y. If m∠Z = 30°. What is the length of YZ (in cm), if ZX = 9 cm?

A) 6√3 B) 9√3/2
C) 3√3 D) 18
 
Answer & Explanation Answer: B) 9√3/2

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