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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:

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:

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:

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:

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:

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 length of the common chord of two intersecting circles is 12 cm. If the diameters of the circles are 15 cm and 13 cm, then what is the distance (in cm) between their centers?

A) 7/2 B) 7
C) 7√2 D) 14
 
Answer & Explanation Answer: B) 7

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