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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:

Two adjacent sides of a parallelogram are 21 cms and 20 cms. The diagonal joining the end points of these two sides is 29 cms. The area of the parallelogram (in sq.cms) is

A) 240 B) 120
C) 210 D) 420
 
Answer & Explanation Answer: D) 420

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Q:

Possible length of the three sides of a triangle are :­

A) 2 cm , 3 cm , 6 cm B) 3 cm , 4 cm , 5 cm
C) 2.5 cm , 3.5 cm , 6 cm D) 4 cm , 4 cm , 9 cm
 
Answer & Explanation Answer: B) 3 cm , 4 cm , 5 cm

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Q:

The height of a cone is 24 cm and the area of the base is 154 cm2 . What is the curved surface area (in cm2) of the cone?

A) 484 B) 550
C) 525 D) 515
 
Answer & Explanation Answer: B) 550

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Q:

T is a point on the common tangents at P of two circles and if TA and TB are resectively the other tangents at A and B to the two circles drawn from the point T then

A) TA = 2 TB B) TA = TB
C) TA = 1/2 TB D) 3TA = TB
 
Answer & Explanation Answer: B) TA = TB

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Q:

The lengths of two diagonals of a rhombus are 24 cm and 32 cm. What is the side (in cm) of the rhombus?

A) 20 B) 40
C) 60 D) 80
 
Answer & Explanation Answer: A) 20

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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:

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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