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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 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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0 980
Q:

The surface areas of three faces of a cuboid sharing a vertex are 20, 32 and 40 sq. mts. What is the volume of the cuboid in cub. m?

A) √3024 B) 184
C) 160 D) 92
 
Answer & Explanation Answer: C) 160

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0 975
Q:

A solid cone of height 24 cm and radius of its base 8 cm is melted to form a solid cylinder of radius 6 cm and height 6 cm. In the whole process what
percent of material is wasted?

A) 48.5 B) 37.5
C) 57.8 D) 64
 
Answer & Explanation Answer: C) 57.8

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0 970
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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2 969
Q:

The radius of base of a solid cylinder is 7 cm and its height is 21 cm. It is melted and converted into small bullets. Each bullet is of same size. Each bullet consisted of two parts viz. a cylinder and a hemisphere on one of its base. The total height of bullet is 3.5 cm and radius of base is 2.1 cm. Approximately how many complete bullets can be obtained?

A) 83 B) 89
C) 74 D) 79
 
Answer & Explanation Answer: A) 83

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1 965
Q:

In ΔDEF, G and H are points on side DE and DF respectively. GH is parallel to EF. If G divides DE in the ratio 1:3 and HF is 7.2 cm, find length of DF?

A) 2.4 cm B) 4.8 cm
C) 3.6 cm D) 9.6 cm
 
Answer & Explanation Answer: D) 9.6 cm

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0 962
Q:

PQRS is a square whose side is 16 cm. What is the value of the side (in cm) of the largest regular octagon that can be cut from the given square?

A) 8 – 4√2 B) 16 + 8√2
C) 16√2 – √16 D) 16 – 8√2
 
Answer & Explanation Answer: C) 16√2 – √16

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0 956
Q:

Curved surface area of a cylinder is 528 sq cm. If circumference of its base is 44 cm, find the height of the cylinder?

A) 12 cm B) 24 cm
C) 36 cm D) 6 cm
 
Answer & Explanation Answer: A) 12 cm

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1 948