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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:

O is the orthocentre of∆ABC, and if ∠BOC = 110° then ∠BAC will be

A) 110° B) 70°
C) 100° D) 90°
 
Answer & Explanation Answer: B) 70°

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0 1712
Q:

In a ∆ABC, BC is extended upto D, ∡ACD =120°, ∡B = 1/2 A. Then ∡A is

A) 60° B) 75°
C) 80° D) 90°
 
Answer & Explanation Answer: C) 80°

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0 1699
Q:

In the given figure, PQ = 30, RS = 24 and OM = 12, then what is the value of ON?

A) 9 B) 12
C) 15 D) 18
 
Answer & Explanation Answer: C) 15

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2 1691
Q:

A cuboid of size 50 cm × 40 cm × 30 cm is cut into 8 identical parts by 3 cuts. What is the total surface area (in cm2) of all the 8 parts?

A) 11750 B) 14100
C) 18800 D) 23500
 
Answer & Explanation Answer: C) 18800

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0 1689
Q:

The ratio of curved surface area and volume of a cylinder is 1 : 7. The ratio of total surface area and volume is 187 : 770. What is the respective ratio of its base radius and height?

A) 5 : 8 B) 4 : 9
C) 3 : 7 D) 7 : 10
 
Answer & Explanation Answer: D) 7 : 10

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0 1687
Q:

In a quadrilateral PQRS, l_S= 90°. A circle (o, r) touches the sides PQ, QR, RS and SP at A, B, C and D respectively. If QR= 38 cm, RS = 25 cm and QA = 27 cm, find 'r'.

A) 16 cm B) 12 cm
C) 14 cm D) 10 cm
 
Answer & Explanation Answer: C) 14 cm

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1 1685
Q:

The perimeter and the length of one of the diagonals of a rhombus is 34 cm 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 1684
Q:

A wooden bowl is in shape of a hollow hemisphere of internal radius 7 cm and thickness 1 cm. What is the total surface area (in sq.cm) of the bowl? (Take:  = 22/7)

A) 710.29 B) 757.43
C) 355.14 D) 908.91
 
Answer & Explanation Answer: B) 757.43

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0 1680