Volume and Surface Area Questions

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:

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:

Length of the sides of a triangle are a, b, c respectively. If a2 + b2 + c2 = ab +bc + ca then the triangle is

A) isosceles B) equilateral
C) scalene D) right­-angled
 
Answer & Explanation Answer: B) equilateral

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Q:

The lengths of diagonals of a rhombus are 24cm and 10cm the perimeter of the rhombus (in cm ) is :

A) 52 B) 56
C) 68 D) 72
 
Answer & Explanation Answer: A) 52

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Q:

If ABCD is a trapezium, AC and BD are the diagonals intersecting each other at point O. Then AC : BD is

A) AB + AD : DC + BC B) AO - OC : OB - OD
C) AB : CD D) AD : BC
 
Answer & Explanation Answer: B) AO - OC : OB - OD

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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:

In an isosceles trapezium ______.

A) Opposite sides are parallel B) Opposite angles are supplementary
C) Opposite angles are not equal D) Diagonals bisect opposite angles
 
Answer & Explanation Answer: B) Opposite angles are supplementary

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Q:

If the radius of the cylinder is decreased by 20%, then by how much percent the height must be increased, so that the volume of the cylinder remains same?

A) 20 B) 36.25
C) 56.25 D) 65
 
Answer & Explanation Answer: C) 56.25

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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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