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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:

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 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:

The whole surface area of a pyramid whose base is a regular polygon is 340 cm2 and area of its base is 100 cm2 . Area of each lateral face is 30 cm2. Then the number of lateral faces is

A) 8 B) 9
C) 7 D) 10
 
Answer & Explanation Answer: A) 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:

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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Q:

What are the co-ordinates of the centroid of a triangle, whose vertices are A(2 , 5), B(-4 , 0) and C(5 , 4)?

A) (-1 , 3) B) (1 , 3)
C) (1 , -3) D) (-1 , -3)
 
Answer & Explanation Answer: B) (1 , 3)

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Q:

Volume of a cylinder is 2310 cubic cm. If circumference of its base is 44 cm, find the curved surface area of the cylinder?

A) 660 sq cm B) 1320 sq cm
C) 1980 sq cm D) 330 sq cm
 
Answer & Explanation Answer: A) 660 sq cm

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Q:

If a regular polygon has 10 sides then the measure of its interior angle is greater than the measure of its exterior angle by how many degrees?

A) 120 B) 132
C) 140 D) 108
 
Answer & Explanation Answer: D) 108

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