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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 curved surface area of a right circular cone is 3080 sq cm and its slant height is 35 cm, find its total surface area?

A) 11088 sq cm B) 1848 sq cm
C) 5544 sq cm D) 2772 sq cm
 
Answer & Explanation Answer: C) 5544 sq cm

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Q:

In ∆XYZ measure of angle Y is 90 deg. If sinX = 4/5, and XY = 6cm, then what is the length (in cm) of side YZ?

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

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Q:

A solid cube is cut into 27 identical cubes. What is the percentage increase in the total surface area?

A) 150 B) 200
C) 300 D) 250
 
Answer & Explanation Answer: B) 200

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0 860
Q:

The total surface area of a hemisphere is 462 sq cm, what is its curved surface area? (Take π = 22/7)

A) 616 sq cms B) 154 sq cms
C) 308 sq cms D) 462 sq cms
 
Answer & Explanation Answer: C) 308 sq cms

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0 858
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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0 857
Q:

10 identical solid spherical balls of radius 3 cm are melted to form a single sphere. In this process 20% of solid is wasted. What is the radius (in cm) of the bigger sphere?

A) 24 B) 12
C) 8 D) 6
 
Answer & Explanation Answer: D) 6

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0 857
Q:

Diameter of wheel of a cycle is 21 cm. The cyclist takes 45 minutes to reach a destination at a speed of 16.5 km/hr. How many revolutions will the wheel make during the journey?

A) 12325 B) 18750
C) 21000 D) 24350
 
Answer & Explanation Answer: B) 18750

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0 856
Q:

The length, breadth and height of a cuboid are in the ratio 19 : 11 : 13. If length is 30 cm more than height, then what is the volume (in cub.cm) of this cuboid?

A) 81510 B) 89665
C) 195300 D) 339625
 
Answer & Explanation Answer: D) 339625

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