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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 cylindrical vessel of radius 7 cm is partially filled with water. By how much will the water level rise if a sphere of radius 6 cm is completely immersed in this water?

A) 11.76 cm B) 17.64 cm
C) 23.52 cm D) 5.88 cm
 
Answer & Explanation Answer: D) 5.88 cm

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0 1012
Q:

How many spherical balls of radius 1 cm can be made by melting a hemisphere of radius 6 cm?

A) 112 B) 108
C) 116 D) 104
 
Answer & Explanation Answer: B) 108

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0 1011
Q:

Calculate the length of the tangent (in cm) which is drawn from a point at a distance of 13 cm from the centre and the largest chord of that circle is 10 cm.

A) 10 B) 12
C) 15 D) 16
 
Answer & Explanation Answer: B) 12

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0 1009
Q:

The length of the radius of a circle with centre O is 5 cm and the length of the chord AB is 8 cm. The distance of the chord AB from the point O is

A) 2 cm B) 3 cm
C) 4 cm D) 15 cm
 
Answer & Explanation Answer: B) 3 cm

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0 1009
Q:

The radius of a wire is decreased to one-third. If volume remains the same, length will increase by

A) 1.5 times B) 3 times
C) 6 times D) 9 times
 
Answer & Explanation Answer: D) 9 times

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0 1008
Q:

Slope of the line AB is 4/3. Co-ordinates of points A and B are (x , -5) and (2 , -3) respectively. What is the value of x?

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

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0 1006
Q:

Calculate the length (in cm) of PQ, if the radius of the circle is 7 cm and the line through the centre O meets the tangent at point Q such that OP = 25 cm.

A) 20 B) 22
C) 24 D) 26
 
Answer & Explanation Answer: C) 24

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0 1006
Q:

The length of two parallel sides of a trapezium are 18 m and 24 m. If its height is 12 m, then what is the area (in sq.m) of the trapezium?

A) 126 B) 252
C) 504 D) 1024
 
Answer & Explanation Answer: B) 252

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