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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:

PQRS is a cyclic quadrilateral and PQ is the diameter of the circle. If ∠RPQ = 38°, then what is the value (in degrees) of ∠PSR?

A) 52 B) 77
C) 128 D) 142
 
Answer & Explanation Answer: C) 128

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0 1955
Q:

ΔABC a right angled triangle has ∠B = 90° and AC is hypotenuse. D is its circumcentre and AB = 3 cms, BC = 4 cms. The value of BD is

A) 3 cms B) 4 cms
C) 2.5 cms D) 5.5 cms
 
Answer & Explanation Answer: C) 2.5 cms

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0 1949
Q:

In the given figure, PQR is an equilateral triangle with side as 12 cm. S and T are the mid points of the sides PQ and PR respectively. What is the area (in sq.cm) of the shaded region?

A) 10√3 B) 12√3
C) 9√3 D) 14√3
 
Answer & Explanation Answer: B) 12√3

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1 1939
Q:

In the given figure, MNOP is a parallelogram. PM is extended to Z. OZ intersects MN and PN at Y and X respectively. If OX = 27 cm and XY = 18 cm, then what is the length (in cm) of YZ?

A) 21.4 B) 22.5
C) 23.8 D) 24.5
 
Answer & Explanation Answer: B) 22.5

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0 1922
Q:

ABCD is a rectangle. P is a point on the side AB as shown in the given figure. If Dp = 13, CP = 10

A) √105 B) √133
C) 12 D) 10
 
Answer & Explanation Answer: A) √105

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1 1918
Q:

A solid sphere of diameter 7 cm is cut into two equal halves. What will be the increase (in cm2) in the total surface area ?

A) 77 B) 154
C) 87 D) 38.5
 
Answer & Explanation Answer: A) 77

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1 1906
Q:

If the curved surface area of a right circular cone is 3080 sq cm and its slant height is 35 cm, find its total surface area?

A) 11088 sq cm B) 1848 sq cm
C) 5544 sq cm D) 2772 sq cm
 
Answer & Explanation Answer: C) 5544 sq cm

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1 1901
Q:

In the given figure,PQ = PS = SR and QPS = 40 deg, then what is the value of QPR (in deg) ?

A) 45 B) 60
C) 75 D) 50
 
Answer & Explanation Answer: C) 75

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1 1900