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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:

In ΔPQR, ∠QPR = 45° and the bisectors of ∠PQR and ∠PRQ meets at O. What is the value (in degrees) of ∠QOR?

A) 107.5 B) 112.5
C) 117.5 D) 122.5
 
Answer & Explanation Answer: B) 112.5

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Q:

In triangle ABC, BAC = 90 deg and AD is perpendicular to BC. If AD = 6cm and BD = 4cm, then the length of BC is

A) 10 cm B) 12 cm
C) 13 cm D) 15 cm
 
Answer & Explanation Answer: C) 13 cm

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Q:

A chord of length 16 cm is drawn in a circle of radius 10 cm. The distance of the chord from the centre of the circle is

A) 8cm B) 6cm
C) 4cm D) 12cm
 
Answer & Explanation Answer: B) 6cm

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Q:

The lengths of diagonals of a rhombus are 24cm and 10cm the perimeter of the rhombus (in cm ) is :

A) 52 B) 56
C) 68 D) 72
 
Answer & Explanation Answer: A) 52

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Q:

Two circles are drawn with the same centre. The circumference of the smaller circle is 44 cm and that of the bigger circle is double the smaller one. What is the area between these two circles?A. 154 square cmB. 308 square cmC. 462 square cmD. 616 square cm

A) 154 square cm B) 308 square cm
C) 462 square cm D) 616 square cm
 
Answer & Explanation Answer: C) 462 square cm

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Q:

In the given figure, PQ is the diameter of the circle. What is the measure (in degrees) of QSR?

A) 23 B) 37
C) 47 D) 57
 
Answer & Explanation Answer: C) 47

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Q:

Find the volume (in cub.cm) of a hemisphere of diameter 21 cm.

A) 2235.5 B) 2425.5
C) 2040 D) 1860
 
Answer & Explanation Answer: B) 2425.5

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Q:

A solid sphere of radius 9 cm is melted to form a sphere of radius 6 cm and a right circular cylinder of same radius. The height of the cylinder so formed is

A) 19 cm B) 21 cm
C) 23 cm D) 25 cm
 
Answer & Explanation Answer: A) 19 cm

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