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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:

The midpoints of AB and AC of a triangle ABC are X and Y respectively. If BC+XY=12 units, then BC­XY is

A) 10 units B) 8 units
C) 6 units D) 4 units
 
Answer & Explanation Answer: D) 4 units

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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:

A circle of diameter 26 cm having the two equal chords of length 10 cm is separated by a distance x cm. Calculate the distance x.

A) 20 B) 22
C) 24 D) 28
 
Answer & Explanation Answer: C) 24

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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:

A solid right circular cone of radius 10 cm and height 8 cm is put inside a cylindrical vessel of radius 11 cm and height 9 cm. How much water in cubic cm will be required to fill the cylindrical vessel completely?

A) 5168.96 cubic cms B) 2584.48 cubic cms
C) 7753.44 cubic cms D) 1292.24 cubic cms
 
Answer & Explanation Answer: B) 2584.48 cubic cms

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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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Q:

Find the curved surface area (in cm2) of a hemisphere of diameter 7 cm.

A) 88 B) 55
C) 77 D) 66
 
Answer & Explanation Answer: C) 77

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Q:

If the measure of the interior angle of a regular polygon is 90 deg greater than the measure of its exterior angle, then how many sides does it have ?

 

A) 8 B) 9
C) 10 D) 12
 
Answer & Explanation Answer: A) 8

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