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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 length of a chord of a circle is equal to that of the radius of the circle, then the angle subtended, in radians, at the centre of the circle by chord is

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

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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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Q:

A cylindrical capsule has hemispherical ends of the radii equal to radius of the cylindrical part. If length of the capsule is 40 m and radius 6 m, what is the total surface area of this capsule?

A) 3017.14 sq mts B) 4525.71 sq mts
C) 1508.57 sq mts D) 754.29 sq mts
 
Answer & Explanation Answer: C) 1508.57 sq mts

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Q:

Δ ABC is right angled at B. If m∠A = 30°. What is the length (in cm) of AB, if AC = 8 cm?

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

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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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Q:

The sum of radii of the two circles is 91 cm and the difference between their area is 2002 cm2 . What is the radius (in cm) of the larger circle?

A) 56 B) 42
C) 63 D) 49
 
Answer & Explanation Answer: D) 49

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Q:

Find the volume (in cm3) of a cube of side 7.5 cm.

A) 421.875 B) 77.145
C) 39.245 D) 24.435
 
Answer & Explanation Answer: A) 421.875

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Q:

A circle of diameter 26 cm having the two equal chords of length 10 cm is separated by a distance x cm. Calculate the distance x.

A) 20 B) 22
C) 24 D) 28
 
Answer & Explanation Answer: C) 24

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