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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:

In a cyclic quadrilateral ABCD , the side AB is extended to a point X. If ∠XBC = 82° and ∠ADB = 47° , then the value of ∠BDC is

A) 40° B) 35°
C) 30° D) 25°
 
Answer & Explanation Answer: B) 35°

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Q:

ABC is an equilateral triangle and P is the orthocenter of the triangle, then what is the value (in degrees) of ∠BPC?

A) 90 B) 120
C) 135 D) 145
 
Answer & Explanation Answer: B) 120

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Q:

ABC is a right angled triangle with angle A = 90 deg. Then the value of cos2A+cos2B+cos2C is

A) 2 B) 1
C) 0 D) 3
 
Answer & Explanation Answer: B) 1

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Q:

ΔPQR has sides PQ and PR measuring 983 and 893 units respectively. How many such triangles are possible with all integral sides?

A) 1876 B) 90
C) 1785 D) 1786
 
Answer & Explanation Answer: C) 1785

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Q:

The height and the total surface area of a right circular cylinder are 4 cm and 8π sq.cm. respectively. The radius of the base of cylinder is

A) (2√2 - 2) cm B) (2 - √2) cm
C) 2 cm D) √2 cm
 
Answer & Explanation Answer: A) (2√2 - 2) cm

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Q:

A regular pyramid has a square base. The height of the pyramid is 22 cm and side of its base is 14 cm. Volume of pyramid is equal to the volume of a sphere. What is the radius (in cm) of the sphere?

A) 493 B) 7
C) 14 D) 983
 
Answer & Explanation Answer: B) 7

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Q:

A chord of length 16 cm is drawn in a circle of radius 10 cm. The distance of the chord from the centre of the circle is

A) 8cm B) 6cm
C) 4cm D) 12cm
 
Answer & Explanation Answer: B) 6cm

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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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