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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 perimeter and the length of one of the diagonals of a rhombus is 34 cm and 8 cm respectively. Find the length of its other diagonal (in cm).

 

A) 7.5 B) 30
C) 22.5 D) 15
 
Answer & Explanation Answer: D) 15

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Q:

In the figure, a circle touches quadrilateral ABCD. If AB = 2x + 3, BC = 3x - 1, CD = x + 6 and DA = x + 4, then what is the value of x?

A) 3 B) 4.5
C) 6 D) 6.5
 
Answer & Explanation Answer: C) 6

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1 1254
Q:

ΔABC is an equilateral triangle and D, E are midpoints of AB and BC respectively. Then the area of ΔABC : the area of the trapezium ADEC is

A) 5:3 B) 4:1
C) 8:5 D) 4:3
 
Answer & Explanation Answer: D) 4:3

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Q:

The least number of square tiles of side 41 cms required to pave the ceiling of a room of size 15m 17cm long and 9m 2 cm broad is:

A) 902 B) 656
C) 738 D) 814
 
Answer & Explanation Answer: D) 814

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0 1238
Q:

If curved surface area of a cylinder is 1386 sq cm and height is 21 cm, what will be its radius? (Take π = 22/7)

A) 21 cms B) 5.25 cms
C) 10.5 cms D) 15.75 cms
 
Answer & Explanation Answer: C) 10.5 cms

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1 1235
Q:

An equilateral triangle ABC is inscribed in a circle of radius 20√3.
The centroid of the triangle ABC is at a distance d from the vertex A. What is d equal to ?

A) 15 cm B) 20 cm
C) 20√3 cm D) 30√3 cm
 
Answer & Explanation Answer: C) 20√3 cm

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0 1227
Q:

In ∆ABC two medians BE and CF intersects at the point O and P,Q are the midpoints of BO and CO respectively. If the length of PQ=3cm, then the length of FE will be

A) 3 cm B) 6 cm
C) 9 cm D) 12 cm
 
Answer & Explanation Answer: A) 3 cm

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0 1225
Q:

In a ∆ABC, BC is extended upto D, ∡ACD =120°, ∡B = 1/2 A. Then ∡A is

A) 60° B) 75°
C) 80° D) 90°
 
Answer & Explanation Answer: C) 80°

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