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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:

Calculate the length of the tangent (in cm) which is drawn from a point at a distance of 13 cm from the centre and the largest chord of that circle is 10 cm.

A) 10 B) 12
C) 15 D) 16
 
Answer & Explanation Answer: B) 12

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Q:

What is the slope of the line parallel to the line passing through the points (5, -1) and (4, -4)?

A) -3 B) -1/3
C) 3 D) 1/3
 
Answer & Explanation Answer: C) 3

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Q:

In ΔABC, ∠B is right angle, D is the mid point of the side AC. If AB = 6 cm, BC = 8cm, then the length of BD is

A) 4 cm B) 5 cm
C) 8 cm D) 12 cm
 
Answer & Explanation Answer: B) 5 cm

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Q:

The volume of a cuboid is 320 cubic cm. Find its total surface area if its length and breadth are 10 cm and 8 cm respectively?

A) 608 sq cms B) 304 sq cms
C) 152 sq cms D) 456 sq cms
 
Answer & Explanation Answer: B) 304 sq cms

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Q:

A cylindrical vessel of height 9 cm and radius 7 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius 10 cm what will be the height of this cone?

A) 26.46 cm B) 39.69 cm
C) 13.23 cm D) 52.92 cm
 
Answer & Explanation Answer: C) 13.23 cm

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Q:

At what point does the line 3x + y = -6 intercept the x-axis?

A) (2,0) B) (-2,0)
C) (0,-6) D) (0,6)
 
Answer & Explanation Answer: B) (-2,0)

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Q:

In a triangle the length of the side opposite the angle which measures 30 degree is 9√3 cm, what is the length of the side opposite to the angle which measures 60 degree?

A) 27 cm B) 9 cm
C) 12√3 cm D) (15√3)/2 cm
 
Answer & Explanation Answer: A) 27 cm

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Q:

If the sum of the interior angles of a regular polygon is 1260 deg , then how many sides does it have?

A) 10 B) 12
C) 15 D) 9
 
Answer & Explanation Answer: D) 9

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