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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:

If the volume of a cylinder is 385 cubic cm and height is 10 cm, find its radius?

A) 7 cm B) 10.5 cm
C) 3.5 cm D) 1.75 cm
 
Answer & Explanation Answer: C) 3.5 cm

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Q:

The sum of radii of the two circles is 91 cm and the difference between their area is 2002 cm2 . What is the radius (in cm) of the larger circle?

A) 56 B) 42
C) 63 D) 49
 
Answer & Explanation Answer: D) 49

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0 961
Q:

PQ is a diameter of a circle with centre O. RS is a chord parallel to PQ subtends an angle of 40° at the centre of the circle. If PR and QS are produced to meet at T, then what will be the measure (in degrees) of ∠PTQ?

A) 55 B) 60
C) 70 D) 90
 
Answer & Explanation Answer: C) 70

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0 957
Q:

The radius of a cylindrical milk container is half its height and surface area of the inner part is 616 sq.cm. The amount of milk that the container can hold, approximately, is [ Use : √5 = 2.23 and π = 22/7 ]

A) 1.42 litres B) 1.53 litres
C) 1.71 litres D) 1.82 litres
 
Answer & Explanation Answer: B) 1.53 litres

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0 957
Q:

What is the reflection of the point (5 , -1) in the line y = 2?

A) (5, -5) B) (-5, -5)
C) (5, 5) D) (-5, 5)
 
Answer & Explanation Answer: C) (5, 5)

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1 954
Q:

In a circle, a chord, 5√2 cm long, makes a right angle at the centre. Then the length of the radius of the circle will be

A) 2.5 cm B) 5 cm
C) 7.5 cm D) 10 cm
 
Answer & Explanation Answer: B) 5 cm

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0 954
Q:

The internal bisectors of ∠Q and ∠R of triangle PQR meet at O. If ∠P = 70°, then what is the measure of ∠QOR (in degrees)?

A) 110 B) 115
C) 125 D) 135
 
Answer & Explanation Answer: C) 125

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0 951
Q:

Two equal circles of radius 3 cm each and distance between their centres is 10 cm. The length of one of their transverse common tangent is

A) 7 cm B) 9 cm
C) 10 cm D) 8 cm
 
Answer & Explanation Answer: D) 8 cm

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0 949