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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 6 cm is partially filled with water. By how much will the water level rise if a sphere of radius 5 cm is completely immersed in this water? (Take π = 22/7)

A) 6.67 cm B) 5.56 cm
C) 6.94 cm D) 4.63 cm
 
Answer & Explanation Answer: D) 4.63 cm

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1 1610
Q:

Due to increase of k% in the side, the area of a square increases by 69%. What is the value of k?

A) 30 B) 33
C) 34.5 D) 35
 
Answer & Explanation Answer: A) 30

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0 1602
Q:

If a cone of radius 3.5 cm and height 9.6 cm is melted and constructed into a cylinder of the same radius, what will be the height of this cylinder? (Take π = 22/7)

A) 3.2 cm B) 6.4 cm
C) 1.6 cm D) 4.8 cm
 
Answer & Explanation Answer: A) 3.2 cm

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1 1597
Q:

10 identical solid spherical balls of radius 3 cm are melted to form a single sphere. In this process 20% of solid is wasted. What is the radius (in cm) of the bigger sphere?

A) 24 B) 12
C) 8 D) 6
 
Answer & Explanation Answer: D) 6

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0 1597
Q:

BE and CF are two altitudes of a triangle ABC. If AB = 6 cm , AC = 5 cm and CF = 4 cm , then the length of BE is

A) 4.8 cm B) 7.5 cm
C) 3.33 cm D) 5.5 cm
 
Answer & Explanation Answer: A) 4.8 cm

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1 1586
Q:

An equilateral triangle ABC is inscribed in a circle of radius 20√3.
The centroid of the triangle ABC is at a distance d from the vertex A. What is d equal to ?

A) 15 cm B) 20 cm
C) 20√3 cm D) 30√3 cm
 
Answer & Explanation Answer: C) 20√3 cm

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0 1567
Q:

The volume of a cube is 166.375 cm3. Find its side (in cm).

A) 6.5 B) 4.5
C) 7.5 D) 5.5
 
Answer & Explanation Answer: D) 5.5

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0 1565
Q:

In triangle PQR, A is the point of intersection of all the altitudes and B is the point of intersection of all the angle bisectors of the triangle. If ∠PBR =105°, then what is the value of ∠PAR (in degrees)?

A) 60 B) 100
C) 105 D) 115
 
Answer & Explanation Answer: A) 60

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0 1564