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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 circle is inscribed in a square. If the length of the diagonal of the square is 14√2 cm, what is the area (in sq cm) of the circle?

A) 308 B) 462
C) 154 D) 616
 
Answer & Explanation Answer: C) 154

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Q:

If ABCD is a trapezium, AC and BD are the diagonals intersecting each other at point O. Then AC : BD is

A) AB + AD : DC + BC B) AO - OC : OB - OD
C) AB : CD D) AD : BC
 
Answer & Explanation Answer: B) AO - OC : OB - OD

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Q:

What is the total surface area (in sq cm) of a hollow cylinder open at both ends, if its length is 22 cm, external radius is 7 cm and thickness is 1 cm? (Take π = 22/7)

A) 1879.43 B) 3758.86
C) 939.715 D) 2819.145
 
Answer & Explanation Answer: A) 1879.43

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Q:

What must be the length (in cm) of the diagonal of a rectangle if its area and breadth are 120 sq.cm and 8 cm respectively ?

A) 34 B) 17
C) 15 D) 30
 
Answer & Explanation Answer: B) 17

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Q:

Find the sum of interior angles of a decagon?

A) 1620° B) 2520°
C) 1800° D) 1440°
 
Answer & Explanation Answer: D) 1440°

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Q:

T is a point on the common tangents at P of two circles and if TA and TB are resectively the other tangents at A and B to the two circles drawn from the point T then

A) TA = 2 TB B) TA = TB
C) TA = 1/2 TB D) 3TA = TB
 
Answer & Explanation Answer: B) TA = TB

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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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Q:

The curved surface area and the diameter of a right circular cylinder are 352 cm² and 14 cm respectively. Find its height (in cm).

A) 9 B) 8
C) 10 D) 11
 
Answer & Explanation Answer: B) 8

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