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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:

Find the total surface area (in cm2) of a cuboid of length, breadth and height of 10.5 cm, 8 cm and 9 cm respectively.

A) 607 B) 767
C) 769 D) 501
 
Answer & Explanation Answer: D) 501

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Q:

Three cubes of iron whose edges are 6cm, 8cm and 10cm respectively are melted and formed into a single cube. The edge of the new cube formed is

A) 12 cm B) 14 cm
C) 16 cm D) 18 cm
 
Answer & Explanation Answer: A) 12 cm

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Q:

Find the total surface area (in cm2) of a right circular cone of diameter 21 cm and slant height 11 cm.

A) 467.5 B) 384
C) 724 D) 709.5
 
Answer & Explanation Answer: D) 709.5

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Q:

If ABCD is a Cyclic Quadrilateral, then the value of Cos2A - Cos2B - Cos2C + Cos2D is

 

 

A) -1 B) 2
C) 1 D) 0
 
Answer & Explanation Answer: C) 1

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Q:

At least two pairs of consecutive angles are congruent in a _____.

A) Parallelogram B) Isosceles trapezium
C) Rhombus D) Kite
 
Answer & Explanation Answer: B) Isosceles trapezium

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0 872
Q:

The length of the two adjacent sides of a rectangle inscribed in a circle are 5 cm and 12 cm respectively. Then the radius of the circle will be

A) 6 cm B) 6.5 cm
C) 8 cm D) 8 .5 cm
 
Answer & Explanation Answer: B) 6.5 cm

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0 870
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:

Two circles touch each other at point X. Two common tangents of the circles meet at point P and none of the tangents passes through X. These tangents touch the larger circle at points B and C. If the radius of the larger circle is 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?

A) 3.5 B) 3.75
C) 4.25 D) 4.45
 
Answer & Explanation Answer: B) 3.75

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