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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:

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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0 1581
Q:

Find the total surface area (in cm2 ) of a hemisphere of diameter 42 cm.

A) 4158 B) 5782
C) 6321 D) 7782
 
Answer & Explanation Answer: A) 4158

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0 1578
Q:

If PQ and PR be the two tangents to a circle with centre O such that ∠QPR = 120° then ∠POQ is

A) 90° B) 45°
C) 30° D) 60°
 
Answer & Explanation Answer: C) 30°

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0 1568
Q:

A solid cone of height 36 cm and radius of base 9 cm is melted to form a solid cylinder of radius 9 cm and height 9 cm. What percent of material is wasted this process?

A) 25 B) 5
C) 0 D) 10
 
Answer & Explanation Answer: A) 25

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1 1564
Q:

An equilateral triangle of area 300 cm2 is cut from its three vertices to form a regular hexagon. Area of hexagon is what percent of the area of triangle?

A) 66.66% B) 33.33%
C) 83.33% D) 56.41%
 
Answer & Explanation Answer: A) 66.66%

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0 1562
Q:

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right –angel. 
What is the area of triangle ADC?

A) 126 SQ.CM B) 124 SQ.CM
C) 122 SQ.CM   D) 120 SQ.CM
 
Answer & Explanation Answer: A) 126 SQ.CM

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1 1562
Q:

If the difference between the measures of the two smaller angles of a right angled triangle is 8°, then the smallest angle is

A) 37° B) 41°
C) 42° D) 49°
 
Answer & Explanation Answer: B) 41°

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0 1561
Q:

Two circles touch externally. The sum of their areas is 130π sq.cm and the distance between their centers is 14 cm. The radius of the bigger circle is

A) 22 cm B) 11 cm
C) 33 cm D) 44 cm
 
Answer & Explanation Answer: B) 11 cm

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0 1561