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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:

In triangle ABC, ∠ABC = 15 deg. D is a point on BC such that AD = BD. What is the measure of ∠ADC (in degrees)?

A) 15 B) 30
C) 45 D) 60
 
Answer & Explanation Answer: B) 30

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1 994
Q:

How many balls of radius 2 cm can be made by melting a bigger ball of diameter 16 cm? (Take π = 22/7)

A) 64 B) 128
C) 32 D) 96
 
Answer & Explanation Answer: A) 64

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1 993
Q:

In the given figure, the length of arc BC of the given circle is 44 cm. If O is the centre of circle, then what is the radius (in cm) of the circle?

A) 7 B) 14
C) 28 D) 35
 
Answer & Explanation Answer: C) 28

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0 992
Q:

In the given figure, P  is the center of the circle. If QS = PR, then what is the ratio of angles RSP to the TPR ?

A) 1 : 4 B) 2 : 5
C) 1 : 3 D) 2 : 7
 
Answer & Explanation Answer: C) 1 : 3

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0 991
Q:

The height of a right circular cylinder is twice its radius of the base. If its height be 6 times its radius of the base, then the volume of the cylinder will be 539 cub.cm more. Assuming Π = 22/7, the height of the cylinder is

A) 5 cm B) 7 cm
C) 9 cm D) 11 cm
 
Answer & Explanation Answer: B) 7 cm

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1 989
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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0 989
Q:

D, E, F are the mid - points of the sides BC , CA and AB respectively of a ΔABC . Then the ratio of the areas of ΔDEF and ΔABC is

A) 1/2 B) 1/4
C) 1/8 D) 1/16
 
Answer & Explanation Answer: B) 1/4

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0 984
Q:

If PQ and PR be the two tangents to a circle with centre O such that ∠QPR = 120° then ∠POQ is

A) 90° B) 45°
C) 30° D) 60°
 
Answer & Explanation Answer: C) 30°

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0 983