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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:

The point of intersection of all the angle bisector of a triangle is ______ of the triangle.

A) Incenter B) Circumcenter
C) Centroid D) Orthocenter
 
Answer & Explanation Answer: A) Incenter

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Q:

Two equal circles of radius 3 cm each and distance between their centres is 10 cm. The length of one of their transverse common tangent is

A) 7 cm B) 9 cm
C) 10 cm D) 8 cm
 
Answer & Explanation Answer: D) 8 cm

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Q:

The external and the internal radii of a hollow right circular cylinder of height 15 cm are 6.75 cm and 5.25 cm respectively. If it is melted to form a solid cylinder of height half of the orignal cylinder, then the radius of the solid cylinder is

A) 6 cm B) 7.25 cm
C) 6.5 cm D) 7 cm
 
Answer & Explanation Answer: A) 6 cm

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Q:

The tangents drawn at points A and B of a circle with centre O, meet at P. If ∠AOB = 120° and AP = 6 cm, then what is the area of triangle (in cm2) APB?

A) 6√3 B) 8√3
C) 9 D) 9√3
 
Answer & Explanation Answer: D) 9√3

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Q:

If an interior of a regular polygon is 170o, then the number of sides of the polygon is

A) 30 B) 20
C) 18 D) 27
 
Answer & Explanation Answer: A) 30

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Q:

What is the curved surface area (in cm²) of a hemisphere of diameter 42 cm?

A) 2332 B) 1778
C) 1556 D) 2772
 
Answer & Explanation Answer: D) 2772

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Q:

Three cubes of iron whose edges are 6cm, 8cm and 10cm respectively are melted and formed into a single cube. The edge of the new cube formed is

A) 12 cm B) 14 cm
C) 16 cm D) 18 cm
 
Answer & Explanation Answer: A) 12 cm

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Q:

At least two pairs of consecutive angles are congruent in a _____.

A) Parallelogram B) Isosceles trapezium
C) Rhombus D) Kite
 
Answer & Explanation Answer: B) Isosceles trapezium

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