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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 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 area and the length of one of the diagonals of a rhombus is 54 cm2 and 9 cm respectively. Find the length of its other diagonal (in cm).

A) 6 B) 24
C) 12 D) 18
 
Answer & Explanation Answer: C) 12

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Q:

ΔABC is similar to ΔDEF. Length of AB is 18 cm and length of the corresponding side DE is 10 cm. What is the ratio of Perimeter of ΔABC : Perimeter of ΔDEF?

A) 5:9 B) 9:5
C) 81:25 D) 25:81
 
Answer & Explanation Answer: B) 9:5

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0 691
Q:

The lengths of the two diagonals of a rhombus are 7 cm and 24 cm. Find the length of its perimeter (in cm).

A) 25 B) 100
C) 75 D) 50
 
Answer & Explanation Answer: D) 50

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Q:

The base of a right prism is a trapezium whose the length of parallel sides are 25 cm and 11 cm and the perpendicular distance between the parallell sides in 16 cm. If the height of the prism is 10 cm, then the volume of the prism is

A) 1440 cu.cm B) 1540 cu.cm
C) 2880 cu.cm D) 960 cu.cm
 
Answer & Explanation Answer: C) 2880 cu.cm

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0 688
Q:

Calculate the length (in cm) of PQ, if the radius of the circle is 7 cm and the line through the centre O meets the tangent at point Q such that OP = 25 cm.

A) 20 B) 22
C) 24 D) 26
 
Answer & Explanation Answer: C) 24

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Q:

A wheel has diameter 84 cm. The number of complete revolution it will take to cover 792 m is

A) 330 B) 300
C) 320 D) 350
 
Answer & Explanation Answer: B) 300

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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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0 686