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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 cylindrical vessel of height 9 cm and radius 7 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius 10 cm what will be the height of this cone?

A) 26.46 cm B) 39.69 cm
C) 13.23 cm D) 52.92 cm
 
Answer & Explanation Answer: C) 13.23 cm

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Q:

In a triangle the length of the side opposite the angle which measures 60° is 15 cm, what is the length of the side opposite to the angle which measures 90°? 

A) 15 cm B) (15√3)/2 cm
C) 10√3 cm D) 10 cm
 
Answer & Explanation Answer: C) 10√3 cm

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Q:

The line parallel to the BC of the triangle ABC divides the other two sides at the point D and E in such a way that AB=3AD. Calculate the ratio of DE and BC.

 

A) 1:6 B) 1:4
C) 1:3 D) 3:1
 
Answer & Explanation Answer: C) 1:3

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Q:

Point A (2, 1) divides segment BC in the ratio 2:3. Co-ordinates of B are (1, -3) and C are (4, y). What is the value of y?

A) 8 B) -7
C) -8 D) 7
 
Answer & Explanation Answer: D) 7

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Q:

Two regular polygons are such that the ratio between their number of sides is 1:2 and the ratio of measures of their interior angles is 3:4. Then the number of sides of each polygon are

A) 10, 20 B) 4, 8
C) 3, 6 D) 5, 10
 
Answer & Explanation Answer: D) 5, 10

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Q:

If the sum of the interior angles of a regular polygon is 1260 deg , then how many sides does it have?

A) 10 B) 12
C) 15 D) 9
 
Answer & Explanation Answer: D) 9

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Q:

If the side of the equilateral triangle is 6√3 cm, then what is length (in cm) of the circum radius of that triangle?

 

A) 4 B) 6
C) 8 D) 12
 
Answer & Explanation Answer: B) 6

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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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