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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:

One internal angle of a rhombus of side 12 cm is 120°. What is the length of its longer diagonal?

A) 6√3 cm B) 12√2 cm
C) 6√2 cm D) 12√3 cm
 
Answer & Explanation Answer: D) 12√3 cm

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Q:

An angle is greater than its complementary by 20°. What will be the measure of the angle?

A) 55° B) 35°
C) 100° D) 80°
 
Answer & Explanation Answer: A) 55°

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Q:

Curved surface area of a cylinder is 440 sq cm. If circumference of its base is 44 cm, what is the volume of the cylinder? (Take π = 22/7)

A) 1540 cubic cm B) 3080 cubic cm
C) 770 cubic cm D) 2310 cubic cm
 
Answer & Explanation Answer: A) 1540 cubic cm

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Q:

The volume of a right circular cone, whose radius of the base is same as its altitude, and the volume of a sphere are equal. The ratio of the radius of the cone to the radius of the sphere is

 

A) 33 : 23 B) 2 : 1
C) 1 : 1 D) 43 : 1
 
Answer & Explanation Answer: D) 43 : 1

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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:

Two circles touch each other internally. The radius of the smaller circle is 6 cm and the distance between the centre of two circles is 3 cm. The radius of the larger circle is

A) 7.5 cm B) 9 cm
C) 8 cm D) 10 cm
 
Answer & Explanation Answer: B) 9 cm

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Q:

A prism has a regular hexagonal base with side 6 cm. If the total surface area of prism is 216√3 cm2, then what is the height (in cm) of prism?

A) 3√3 B)  6√3
C) 6 D) 3
 
Answer & Explanation Answer: A) 3√3

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Q:

Choose the correct option for the figure shown below.

A) AD = AF B) BD = BE
C) CE = FC D) All option are correct
 
Answer & Explanation Answer: D) All option are correct

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