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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:

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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Q:

A cone is hollowed out of a solid wooden cube of side 6 cm. The diameter and height of the cone is same as the side of the cube. What is the volume of the remaining cube?

A) 159.42 cubic cms B) 323.15 cubic cms
C) 106.33 cubic cms D) 210.66 cubic cms
 
Answer & Explanation Answer: A) 159.42 cubic cms

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Q:

What is the slope of the line parallel to the line passing through the points (6,­3) and (2,­1)?

A) -1/2 B) -1
C) 2 D) 1
 
Answer & Explanation Answer: A) -1/2

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Q:

If the curved surface area of a right circular cone is 10010 sq cm and its slant height is 91 cm, find its total surface area.

A) 27720 sq cm B) 4620 sq cm
C) 6930 sq cm D) 13860 sq cm
 
Answer & Explanation Answer: D) 13860 sq cm

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Q:

Two tangents PA and PB are drawn to a circle of centre O in such a way that angle AOB = 120 deg. Calculate the value of angle APB.

A) 40 deg B) 50 deg
C) 60 deg D) 80 deg
 
Answer & Explanation Answer: C) 60 deg

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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 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:

At what point does the line 3x + y = -6 intercept the x-axis?

A) (2,0) B) (-2,0)
C) (0,-6) D) (0,6)
 
Answer & Explanation Answer: B) (-2,0)

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