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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:

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:

A cone of radius 3.5 cm and height 12 cm is completely filled with water. This water is emptied into an empty cylindrical vessel of radius 7 cm. What will be the height of water in this vessel?

A) 2 cm B) 0.33 cm
C) 0.5 cm D) 1 cm
 
Answer & Explanation Answer: D) 1 cm

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Q:

A square is inscribed in a circle. If the side of the square is 14 cm, what is the area (in sq.cm) of the circle?

A) 49π B) 77π
C) 121π D) 98π
 
Answer & Explanation Answer: D) 98π

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Q:

The tangents drawn at points A and B of a circle with centre O, meet at P. If ∠AOB = 120° and AP = 6 cm, then what is the area of triangle (in cm2) APB?

A) 6√3 B) 8√3
C) 9 D) 9√3
 
Answer & Explanation Answer: D) 9√3

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Q:

If a cylinder of radius 7 cm and height 9 cm is melted and constructed into a cone of the same radius, what will be the height of this cone?

A) 54 cm B) 9 cm
C) 27 cm D) 13.5 cm
 
Answer & Explanation Answer: C) 27 cm

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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:

Find length of the arc whose central angle is 90° and radius of the circle is 3.5 cm?

A) 11 cm B) 5.5 cm
C) 16.5 cm D) 22 cm
 
Answer & Explanation Answer: B) 5.5 cm

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Q:

A solid brass sphere of radius 2.1 dm is converted into a right circular cylindrical rod of length 7cm. The ratio of total surface areas of the rod to the sphere is

A) 3:1 B) 1:3
C) 7:3 D) 3:7
 
Answer & Explanation Answer: C) 7:3

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