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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:

Suppose that the medians BD, CE and AF of a triangle ABC meet at G. Then AG: GF is

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

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Q:

The volume of a right circular cone, with a base radius the same as its altitude, and the volume of a hemisphere are equal. The ratio of the radii of the cone to the hemisphere is

A) 2 : 1 B) √2 : 1
C) 23 : 1 D) 33 : 23
 
Answer & Explanation Answer: C) 23 : 1

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Q:

The lengths of two parallel sides of a trapezium are 21 cm and 9 cm. If its height is 10 cm, then what is the area (in cm2) of the trapezium?

A) 35 B) 75
C) 150 D) 225
 
Answer & Explanation Answer: C) 150

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Q:

Two circles with centres P and Q touch each other externally. A straight line drawn through the point of contact intersects the circle with centre P at A and the circle with centre Q at B. Then, which of the following is true?

A) AP = BQ B) AP | BQ
C) AP || BQ D) AP = 1⁄2 BQ
 
Answer & Explanation Answer: C) AP || BQ

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Q:

Analyze the figure shown below in which DE || BC and the other dimensions are as follows: AD=3 cm, BD=4 cm, AE=4.4 cm and DE=6 cm. Calculate the length (in cm) of BC.

A) 6 B) 8
C) 12 D) 14
 
Answer & Explanation Answer: D) 14

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Q:

The co-ordinates of the centroid of a triangle ABC are (-1 , 4). What are the co-ordinates of vertex C if co-ordinates of A and B are (-3 , -1) and (3 , 5) respectively?

A) (-3 , 8) B) (3 , 8)
C) (-3 , -8) D) (3 , -8)
 
Answer & Explanation Answer: A) (-3 , 8)

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Q:

A cylindrical vessel of height 9 cm and radius 7 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius 10 cm what will be the height of this cone?

A) 26.46 cm B) 39.69 cm
C) 13.23 cm D) 52.92 cm
 
Answer & Explanation Answer: C) 13.23 cm

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Q:

The ratio between the vertical angle and a base angle of an isosceles triangle is 4:3. The value of any one base angle is

A) 18 deg B) 54 deg
C) 72 deg D) 10 deg
 
Answer & Explanation Answer: B) 54 deg

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