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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:

A sphere has the same curved surface area as a cone of vertical height 40 cm and radius 30 cm. The radius of the sphere is

A) 5√5 cm B) 5√3 cm
C) 5√15 cm D) 5√10 cm
 
Answer & Explanation Answer: C) 5√15 cm

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0 1313
Q:

In the given figure, PQ is the diameter of the circle. What is the measure (in degrees) of QSR?

A) 23 B) 37
C) 47 D) 57
 
Answer & Explanation Answer: C) 47

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0 1311
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 1308
Q:

ABC is a right angled triangle with angle A = 90 deg. Then the value of cos2A+cos2B+cos2C is

A) 2 B) 1
C) 0 D) 3
 
Answer & Explanation Answer: B) 1

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0 1307
Q:

The length, breadth and height of a cuboid are 12 cm, 8 cm and 6 cm respectively. The volume of the cuboid is (Use π = 22/7)

A) 1152 cubic cms B) 288 cubic cms
C) 576 cubic cms D) 864 cubic cms
 
Answer & Explanation Answer: C) 576 cubic cms

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0 1306
Q:

A regular square pyramid has side of its base 20 cm and height 45 cm is melted and recast into regular triangular pyramids of equilateral base of side 10 cm and height 10√3 cm. What are the total numbers of regular triangular pyramid?

A) 24 B) 20
C) 27 D) 28
 
Answer & Explanation Answer: A) 24

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0 1302
Q:

In a cyclic quadrilateral ABCD , the side AB is extended to a point X. If ∠XBC = 82° and ∠ADB = 47° , then the value of ∠BDC is

A) 40° B) 35°
C) 30° D) 25°
 
Answer & Explanation Answer: B) 35°

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0 1300
Q:

BD and CE are two medians of the triangle ABC. If EO = 7 cm, then the length of CE is

A) 28 cm B) 14 cm
C) 21 cm D) 35 cm
 
Answer & Explanation Answer: C) 21 cm

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0 1300