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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:

A cone of height 12 cm and diameter 10 cm is mounted on a hemisphere of the same diameter. What is the volume of the solid thus formed?

A) 384.13 sq cm B) 576.19 sq cm
C) 192.06 sq cm D) 288.1 sq cm
 
Answer & Explanation Answer: B) 576.19 sq cm

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Q:

A solid right circular cone of radius 10 cm and height 8 cm is put inside a cylindrical vessel of radius 11 cm and height 9 cm. How much water in cubic cm will be required to fill the cylindrical vessel completely?

A) 5168.96 cubic cms B) 2584.48 cubic cms
C) 7753.44 cubic cms D) 1292.24 cubic cms
 
Answer & Explanation Answer: B) 2584.48 cubic cms

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Q:

In which of the following quadrilaterals opposite angles are supplementary?

A) Rhombus B) Parallelogram
C) Trapezium D) Cyclic quadrilateral
 
Answer & Explanation Answer: D) Cyclic quadrilateral

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Q:

The diagonal of a square is 10 cm. What is the length (in cm) of its side?

A) 5 B) 5√2
C) 10√2 D) 5/√2
 
Answer & Explanation Answer: B) 5√2

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Q:

A right circular conical structure stands on a circular base of 21m diameter and is 14m in height. The total cost of colour washing for its curved surface at Rs. 6 per sq. m. is
(Take Π = 22/7 )

A) 4365 B) 4465
C) 3465 D) 3365
 
Answer & Explanation Answer: C) 3465

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Q:

If the volumes of two right circular cones are in the ratio 1:4 and their diameters of bases in the ratio 4:5, then their heights will be in the ratio:

A) 1: 5 B) 4:25
C) 16:25 D) 25:64
 
Answer & Explanation Answer: D) 25:64

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Q:

The length of one side of a rhombus is 41 cm and its area is 720 sq.cm. What is the sum of the lengths of its diagonals?

A) 82 cm B) 90 cm
C) 98 cm D) 80 cm
 
Answer & Explanation Answer: C) 98 cm

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Q:

A chord of a circle is equal to its radius. A tangent is drawn to the circle at an extremity of the chord. The angle between the tangent and the chord is

A) 30° B) 45°
C) 60° D) 75°
 
Answer & Explanation Answer: A) 30°

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