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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:

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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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 1392
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 1387
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 1387
Q:

The ratio of curved surface area and volume of a cylinder is 1 : 7. The ratio of total surface area and volume is 187 : 770. What is the respective ratio of its base radius and height?

A) 5 : 8 B) 4 : 9
C) 3 : 7 D) 7 : 10
 
Answer & Explanation Answer: D) 7 : 10

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0 1380
Q:

PQRS is a square whose side is 16 cm. What is the value of the side (in cm) of the largest regular octagon that can be cut from the given square?

A) 8 – 4√2 B) 16 + 8√2
C) 16√2 – √16 D) 16 – 8√2
 
Answer & Explanation Answer: C) 16√2 – √16

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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 1378
Q:

The perimeter and the length of one of the diagonals of a rhombus is 34 cm and 8 cm respectively. Find the length of its other diagonal (in cm).

 

A) 7.5 B) 30
C) 22.5 D) 15
 
Answer & Explanation Answer: D) 15

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