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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 chord AB of a circle of centre O subtends an angle θ with the tangent at A to the circle. Then measure of∠ABO is

A) θ B) 90° - θ
C) 90° + θ D) 2 (180° - θ)
 
Answer & Explanation Answer: B) 90° - θ

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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 1418
Q:

In the given fig, ST||RP, then what is the value of supplementary angle y (in deg)?

A) 10 B) 60
C) 100 D) 170
 
Answer & Explanation Answer: C) 100

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0 1417
Q:

If ΔABC is an equilateral triangle of side 16 cm, then the length of altitude is

A) 2√3 cm B)  4√3 cm
C) 8√3 cm D)  5√3 cm
 
Answer & Explanation Answer: C) 8√3 cm

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2 1411
Q:

If O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O, a point P is taken. From this point, two tangents PQ and PR are drawn to the circle. Then , the area of quadrilateral PQOR is

A) 60 cm2 B) 32.5 cm2
C) 65 cm2 D) 30 cm2
 
Answer & Explanation Answer: A) 60 cm2

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0 1410
Q:

If the length of a chord of a circle is equal to that of the radius of the circle, then the angle subtended, in radians, at the centre of the circle by chord is

A) 1 B) ∏/2
C) ∏/3 D) ∏/4
 
Answer & Explanation Answer: C) ∏/3

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0 1409
Q:

T is a point on the common tangents at P of two circles and if TA and TB are resectively the other tangents at A and B to the two circles drawn from the point T then

A) TA = 2 TB B) TA = TB
C) TA = 1/2 TB D) 3TA = TB
 
Answer & Explanation Answer: B) TA = TB

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Q:

In an isosceles triangle ABC, AB = AC and ∠A = 80°. The bisector of ∠B and ∠C meet at D. The ∠BDC is equal to

A) 90° B) 100°
C) 130° D) 80°
 
Answer & Explanation Answer: C) 130°

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