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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 a circle of radius 8 cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC?

A) 2√6 cm B) 3√6 cm
C) 3√7 cm D) 6√7 cm
 
Answer & Explanation Answer: D) 6√7 cm

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2 2120
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 2093
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 2091
Q:

In the given figure, ABC is an equilateral triangle. Two circles of radius 4 cm and 12 cm are inscribed in the triangle. What is the side (in cm) of an equilateral triangle ?

A) 32/√3 B) 32√3
C) 64/√3 D) None
 
Answer & Explanation Answer: D) None

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0 2075
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 2071
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 2067
Q:

Three toys are in a shape of cylinder, hemisphere and cone. The three toys have same base. Height of each toy is 2√2 cm. What is the ratio of the total surface areas of cylinder, hemisphere and cone respectively?

A) 4 : 3 : [(√2) + 1] B) 4 : 3 : [2 + (√2)]
C) 4 : 3 : 2√2 D) 2 : 1 : (1 + √2)
 
Answer & Explanation Answer: A) 4 : 3 : [(√2) + 1]

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0 2066
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 2066