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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:

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 1556
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 1533
Q:

The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.
If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?

A) 572 cub.cm B) 728 cub.cm
C) 1144 cub.cm D) None of the above
 
Answer & Explanation Answer: C) 1144 cub.cm

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2 1524
Q:

A solid cone of height 24 cm and radius of its base 8 cm is melted to form a solid cylinder of radius 6 cm and height 6 cm. In the whole process what
percent of material is wasted?

A) 48.5 B) 37.5
C) 57.8 D) 64
 
Answer & Explanation Answer: C) 57.8

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0 1516
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 1512
Q:

PQRS is a square, M is the mid-point of PQ and N is a point on QR such that NR is two-third of QR. If the area of ΔMQN is 48 cm2 , then what is the length (in cm) of PR ?

A) 12√2 B) 12
C) 24 D) 24√2
 
Answer & Explanation Answer: D) 24√2

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1 1510
Q:

Three consecutive angles of a cycle quadrilateral are in the ratio of 1 : 4 : 5 . The measure of fourth angle is

A) 120° B) 60°
C) 30° D) 80°
 
Answer & Explanation Answer: B) 60°

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1 1487
Q:

O is the circumcentre of ΔABC. If AO = 8 cm, then the length of BO is

A) 12 cm B) 3 cm
C) 6 cm D) 8 cm
 
Answer & Explanation Answer: D) 8 cm

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