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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 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:

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:

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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Q:

Curved surface area of a cylinder is 660 sq cm. If circumference of its base is 44 cm, find the volume of the cylinder?

A) 4620 cubic cm B) 2310 cubic cm
C) 6930 cubic cm D) 1155 cubic cm
 
Answer & Explanation Answer: B) 2310 cubic cm

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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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