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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:

A cylindrical vessel of radius 6 cm is partially filled with water. By how much will the water level rise if a sphere of radius 5 cm is completely immersed in this water? (Take π = 22/7)

A) 6.67 cm B) 5.56 cm
C) 6.94 cm D) 4.63 cm
 
Answer & Explanation Answer: D) 4.63 cm

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1 1314
Q:

In ∆XYZ measure of angle Y is 90 deg. If sinX = 4/5, and XY = 6cm, then what is the length (in cm) of side YZ?

A) 10 B) 5
C) 8 D) 4
 
Answer & Explanation Answer: C) 8

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0 1311
Q:

ΔABC is an equilateral triangle and D, E are midpoints of AB and BC respectively. Then the area of ΔABC : the area of the trapezium ADEC is

A) 5:3 B) 4:1
C) 8:5 D) 4:3
 
Answer & Explanation Answer: D) 4:3

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1 1307
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 1307
Q:

A closed wooden rectangular box made of 1 cm thick wood has the following outer dimensions : length 22 cm, breadth 17 cm, and height 12cm. It is filled to capacity with cement. What is the volume of the cement in the box?

 

A) 1488 cu. cm B) 3000 cu. cm
C) 4488 cu. cm D) 2880 cu. cm
 
Answer & Explanation Answer: B) 3000 cu. cm

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1 1306
Q:

In a triangle PQR, S and T are the points on PQ and PR respectively, such that ST II QR and PS/SQ=3/5,PR =6cm, then PT is

A) 2 cm B) 2.25 cm
C) 3.5 cm D) 4 cm
 
Answer & Explanation Answer: B) 2.25 cm

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0 1298
Q:

The least number of square tiles of side 41 cms required to pave the ceiling of a room of size 15m 17cm long and 9m 2 cm broad is:

A) 902 B) 656
C) 738 D) 814
 
Answer & Explanation Answer: D) 814

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0 1290
Q:

In the given figure, AB, AE, EF, FG and GB are semicircles. AB = 56 cm and AE = EF = FG = GB. What is the area (in sq.cm) of the shaded region?

 

A) 414.46 B) 382.82
C) 406.48 D) 394.24
 
Answer & Explanation Answer: D) 394.24

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0 1286