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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 total surface area (in cm2) of a cube of side 3.5 cm.

A) 91.7 B) 64
C) 88 D) 73.5
 
Answer & Explanation Answer: D) 73.5

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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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Q:

If the measure of the interior angle of a regular polygon is 100 deg greater than the measure of its exterior angle then how many sides does it have?

 

A) 10 B) 12
C) 9 D) 15
 
Answer & Explanation Answer: C) 9

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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:

In a triangle ABC, right angled at B, BC = 15 cm and AB = 8 cm. A circle is inscribed in triangle ABC. Then the radius of the circle is :

A) 3 cm B) 2 cm
C) 4 cm D) 1 cm
 
Answer & Explanation Answer: A) 3 cm

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Q:

How many spherical balls of radius 1 cm can be made by melting a hemisphere of radius 6 cm?

A) 112 B) 108
C) 116 D) 104
 
Answer & Explanation Answer: B) 108

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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 sum of the lengths of the edges of a cube is equal to half the perimeter of a square. If the numerical value of the volume pf the cube is equal to one-sixth of the numerical value of the area of the square, then the length of one side of the square is

A) 31.5 units B) 36 units
C) 27 units D) 18 units
 
Answer & Explanation Answer: B) 36 units

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