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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:

Curved surface area of a cylinder is 528 sq cm. If circumference of its base is 44 cm, find the height of the cylinder?

A) 12 cm B) 24 cm
C) 36 cm D) 6 cm
 
Answer & Explanation Answer: A) 12 cm

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Q:

Three solid spheres have their radii r1, r2 and r3. The spheres are melted to form a solid sphere of bigger radius. Then the radius of the new sphere is

A) r1+r2+r3 B) r12+r22+r3212
C) r13+r23+r3313 D) r14+r24+r3414
 
Answer & Explanation Answer: C) r13+r23+r3313

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0 1734
Q:

The length of diagonal BD of a parallelogram ABCD is 36 cm. P and Q are the centroids of triangle ABC and triangle ADC respectively. What is the length (in cm) of PQ?

A) 6 B) 9
C) 12 D) 18
 
Answer & Explanation Answer: C) 12

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0 1732
Q:

The ratio of the volume of two cylinders is 7 : 3 and the ratio of their heights is 7 : 9. If the area of the base of the second cylinder is 154 sq. cm, then what will be the radius (in cm) of the first cylinder?

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

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0 1727
Q:

The measure of the four successive angles of a quadrilateral are in the ratio 7 : 11 : 7 : 11. The quadrilateral is a ______.

A) trapezium B) rectangle
C) parallelogram D) square
 
Answer & Explanation Answer: C) parallelogram

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0 1718
Q:

In the given figure, AB, AE, EF, FG and GB are semicircles. AB = 56 cm and AE = EF = FG = GB. What is the area (in sq.cm) of the shaded region?

 

A) 414.46 B) 382.82
C) 406.48 D) 394.24
 
Answer & Explanation Answer: D) 394.24

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0 1713
Q:

ΔABC is an equilateral triangle and D, E are midpoints of AB and BC respectively. Then the area of ΔABC : the area of the trapezium ADEC is

A) 5:3 B) 4:1
C) 8:5 D) 4:3
 
Answer & Explanation Answer: D) 4:3

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1 1712
Q:

If curved surface area of a cylinder is 1386 sq cm and height is 21 cm, what will be its radius? (Take π = 22/7)

A) 21 cms B) 5.25 cms
C) 10.5 cms D) 15.75 cms
 
Answer & Explanation Answer: C) 10.5 cms

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