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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:

In ΔABC, AD is the median and AD = (1/2)BC. If ∠ACD = 40°, then what is the value (in degrees) of ∠DAB?

A) 30 B) 40
C) 50 D) 60
 
Answer & Explanation Answer: C) 50

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Q:

A regular hexagonal base prism has height 8 cm and side of base is 4 cm. What is the total surface area (in cm2) of the prism?

A) 54(3 + √3) B) 36(3 + √3)
C) 48(4 + √3) D) 24(4 + √3)
 
Answer & Explanation Answer: C) 48(4 + √3)

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0 1110
Q:

The radius of the circle circumscribing the three vertices of an equilateral triangle is 12 cm. Determine the height (in cm) of the equilateral triangle

A) 12 B) 14
C) 18 D) 20
 
Answer & Explanation Answer: C) 18

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4 1109
Q:

The base of a prism is in the shape of an equilateral triangle. If the perimeter of the base is 18 cm and the height of the prism is 20 cm, then what is the volume (in cm3) of the prism?

A) 60√3 B) 30√6
C) 60√2 D) not know
 
Answer & Explanation Answer: D) not know

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0 1109
Q:

In the given figure, ABCD is a square, BCXYZ is a regular pentagon and ABE is an  equilateral triangle. What is the value in deg of EBZ?

A) 102 B) 98
C) 78 D) 64
 
Answer & Explanation Answer: A) 102

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0 1108
Q:

If ΔABC is an equilateral triangle of side 16 cm, then the length of altitude is

A) 2√3 cm B)  4√3 cm
C) 8√3 cm D)  5√3 cm
 
Answer & Explanation Answer: C) 8√3 cm

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2 1106
Q:

A solid brass sphere of radius 2.1 dm is converted into a right circular cylindrical rod of length 7cm. The ratio of total surface areas of the rod to the sphere is

A) 3:1 B) 1:3
C) 7:3 D) 3:7
 
Answer & Explanation Answer: C) 7:3

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0 1106
Q:

ABCD is an isosceles trapezium such that AD||BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?

A) 36 B) 44
C) 88 D) 144
 
Answer & Explanation Answer: B) 44

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