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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:

The length of the diagonal and the breadth of a rectangle are 29 cm and 20 cm respectively. Find its perimeter (in cm).

 

A) 164 B) 82
C) 21 D) 42
 
Answer & Explanation Answer: B) 82

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Q:

The length and breadth of a rectangular piece of a land are in a ratio 5:3. The owner spent Rs. 6000 for surrounding it from all sides at Rs.7.50 per metre. The difference between its length and breadth is

A) 50 metres B) 100 metres
C) 150 metres D) 250 metres
 
Answer & Explanation Answer: B) 100 metres

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0 745
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:

If the in radius of the equilateral triangle is 8 cm then what is the value of circum radius (in cm) of the triangle?

A) 8 B) 16
C) 18 D) 20
 
Answer & Explanation Answer: B) 16

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0 740
Q:

In a triangle, the length of the side opposite the angle which measures 45° is 16 cm, what is the length of the side opposite to the angle which measures 90°? 

A) 8√3 cm B) 16√2 cm
C) 8 cm D) 16√3 cm
 
Answer & Explanation Answer: B) 16√2 cm

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Q:

A cylindrical vessel of height 7 cm and radius 5 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius 8 cm what will be the height of this cone?

A) 8.2 cm B) 16.4 cm
C) 24.6 cm D) 32.8 cm
 
Answer & Explanation Answer: A) 8.2 cm

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Q:

Which of the following triangle is formed when the triangle has all the three medians of equal length?0

A) Scalene B) Isosceles
C) Equilateral D) Right angled
 
Answer & Explanation Answer: C) Equilateral

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Q:

In the two triangles ABC and DEF the sides AB = DE and BC = EF. Which of the following option is correct which results in the ∆ABC ≅∆DEF?

 

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

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