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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 height 7 cm and radius 5 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius 8 cm what will be the height of this cone?

A) 8.2 cm B) 16.4 cm
C) 24.6 cm D) 32.8 cm
 
Answer & Explanation Answer: A) 8.2 cm

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0 1014
Q:

In a triangle ABC, ∠A = 70°, ∠B = 80° and D is the incentre of ΔABC. ∠ACB = 2x° and ∠BDC = y°. The values of x and y, respectively are

A) 15, 130 B) 15, 125
C) 35, 40 D) 30, 150
 
Answer & Explanation Answer: B) 15, 125

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0 1013
Q:

If the edge of a cube is increased by 2 cm, the volume will increase by 488 cub.cm. What then will be the length of each edge of the cube?

A) 6 cm B) 8 cm
C) 9 cm D) 7 cm
 
Answer & Explanation Answer: B) 8 cm

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0 1011
Q:

The point of the intersection of three medians is known as the ____________.

A) circum-centre B) in-center
C) centroid D) orthocenter
 
Answer & Explanation Answer: C) centroid

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0 1009
Q:

Find the volume (in cm3) of a cuboid of length, breadth and height of 8.5 cm, 6 cm and 7 cm respectively.

A) 524 B) 626
C) 603 D) 357
 
Answer & Explanation Answer: D) 357

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1 1008
Q:

Find the curved surface area (in cm2) of a right circular cylinder of diameter 7 cm and height 6 cm.

A) 132 B) 110
C) 92 D) 154
 
Answer & Explanation Answer: A) 132

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0 1005
Q:

In a triangle, the length of the side opposite the angle which measures 45° is 16 cm, what is the length of the side opposite to the angle which measures 90°? 

A) 8√3 cm B) 16√2 cm
C) 8 cm D) 16√3 cm
 
Answer & Explanation Answer: B) 16√2 cm

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0 1004
Q:

The length of the diameter of the circle is 10 cm and length of the chord drawn in a circle is 6 cm. Find the distance (in cm) of chord from the center.

 

A) 10 B) 8
C) 6 D) 4
 
Answer & Explanation Answer: D) 4

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0 1004