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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:

In the figure, a circle touches quadrilateral ABCD. If AB = 2x + 3, BC = 3x - 1, CD = x + 6 and DA = x + 4, then what is the value of x?

A) 3 B) 4.5
C) 6 D) 6.5
 
Answer & Explanation Answer: C) 6

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1 1634
Q:

A cuboid of size 50 cm × 40 cm × 30 cm is cut into 8 identical parts by 3 cuts. What is the total surface area (in cm2) of all the 8 parts?

A) 11750 B) 14100
C) 18800 D) 23500
 
Answer & Explanation Answer: C) 18800

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0 1626
Q:

In a quadrilateral PQRS, l_S= 90°. A circle (o, r) touches the sides PQ, QR, RS and SP at A, B, C and D respectively. If QR= 38 cm, RS = 25 cm and QA = 27 cm, find 'r'.

A) 16 cm B) 12 cm
C) 14 cm D) 10 cm
 
Answer & Explanation Answer: C) 14 cm

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1 1625
Q:

The ratio of curved surface area and volume of a cylinder is 1 : 7. The ratio of total surface area and volume is 187 : 770. What is the respective ratio of its base radius and height?

A) 5 : 8 B) 4 : 9
C) 3 : 7 D) 7 : 10
 
Answer & Explanation Answer: D) 7 : 10

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0 1618
Q:

In a ∆ABC, BC is extended upto D, ∡ACD =120°, ∡B = 1/2 A. Then ∡A is

A) 60° B) 75°
C) 80° D) 90°
 
Answer & Explanation Answer: C) 80°

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0 1613
Q:

A closed wooden rectangular box made of 1 cm thick wood has the following outer dimensions : length 22 cm, breadth 17 cm, and height 12cm. It is filled to capacity with cement. What is the volume of the cement in the box?

 

A) 1488 cu. cm B) 3000 cu. cm
C) 4488 cu. cm D) 2880 cu. cm
 
Answer & Explanation Answer: B) 3000 cu. cm

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1 1612
Q:

In the given figure, PQ = 30, RS = 24 and OM = 12, then what is the value of ON?

A) 9 B) 12
C) 15 D) 18
 
Answer & Explanation Answer: C) 15

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2 1611
Q:

The perimeter and the length of one of the diagonals of a rhombus is 34 cm and 8 cm respectively. Find the length of its other diagonal (in cm).

 

A) 7.5 B) 30
C) 22.5 D) 15
 
Answer & Explanation Answer: D) 15

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0 1611