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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:

The volume of metallic cylindrical pipe of uniform thickness is 748 c.c. Its length is 14 cm and its external radius is 9 cm. The thickness of the pipe is

A) 0.5 cm B) 1.5 cm
C) 1 cm D) 2 cm
 
Answer & Explanation Answer: C) 1 cm

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Q:

A regular square pyramid has side of its base 20 cm and height 45 cm is melted and recast into regular triangular pyramids of equilateral base of side 10 cm and height 10√3 cm. What are the total numbers of regular triangular pyramid?

A) 24 B) 20
C) 27 D) 28
 
Answer & Explanation Answer: A) 24

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Q:

In the given figure, if AD = 12 cm, AE = 8 cm and EC = 14 cm, then what is the value of BD in cm?

A) 50/3 B) 15
C) 8/3 D) 44/3
 
Answer & Explanation Answer: C) 8/3

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Q:

In an isosceles triangle ABC, AB = AC, XY || BC. If ∡A = 30, then ∡BXY = 

A) 75° B) 30°
C) 150° D) 105°
 
Answer & Explanation Answer: D) 105°

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Q:

The total surface area of a hemisphere is 462 sq.cm. Find its diameter (in cm).

A) 7 B) 28
C) 21 D) 14
 
Answer & Explanation Answer: D) 14

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Q:

The radius and height of a solid cylinder are increased by 2% each. What will be the approximate percentage increase in volume?

A) 6.76 B) 5.88
C) 6.12 D) 3.34
 
Answer & Explanation Answer: C) 6.12

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Q:

In triangle ABC, ∠ABC = 90°. BP is drawn perpendicular to AC. If ∠BAP = 50°, then what is the value (in degrees) of ∠PBC?

A) 30 B) 45
C) 50 D) 60
 
Answer & Explanation Answer: C) 50

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Q:

In a circle, a chord, 5√2 cm long, makes a right angle at the centre. Then the length of the radius of the circle will be

A) 2.5 cm B) 5 cm
C) 7.5 cm D) 10 cm
 
Answer & Explanation Answer: B) 5 cm

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