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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 solid cone of height 36 cm and radius of base 9 cm is melted to form a solid cylinder of radius 9 cm and height 9 cm. What percent of material is wasted this process?

A) 25 B) 5
C) 0 D) 10
 
Answer & Explanation Answer: A) 25

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Q:

Point A divides segment BC in the ratio 5:1. Co-ordinates of B are (6 ,-4) and C are (0,8). What are the co-ordinates of point A?

A) (-1 , 6) B) (1 , -6)
C) (-1 , -6) D) (1 , 6)
 
Answer & Explanation Answer: D) (1 , 6)

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Q:

In triangle ABC, a line is drawn from the vertex A to a point D on BC. If BC = 9 cm and DC = 3 cm, then what is the ratio of the areas of triangle ABD and triangle ADC respectively?

A) 1 : 1 B) 2 : 1
C) 3 : 1 D) 4 : 1
 
Answer & Explanation Answer: B) 2 : 1

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Q:

In ΔABC, AD is the median and AD = (1/2)BC. If ∠ACD = 40°, then what is the value (in degrees) of ∠DAB?

A) 30 B) 40
C) 50 D) 60
 
Answer & Explanation Answer: C) 50

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Q:

Point P (8 , 5) is the midpoint of segment AB. Co-ordinates of A are (5, y) and B are (x, -3). What is the value of x?

A) -11 B) 11
C) 7 D) -7
 
Answer & Explanation Answer: B) 11

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Q:

The total surface area of a cuboid is 376 sq cm. Find its volume if its length and breadth are 10 cm and 8 cm respectively?

A) 960 cubic cms B) 240 cubic cms
C) 480 cubic cms D) 720 cubic cms
 
Answer & Explanation Answer: C) 480 cubic cms

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Q:

In a Rhombus ABCD, measure of angle CAB is 30°, what is the measure of angle ABC?

A) 60° B) 120°
C) 90° D) 150°
 
Answer & Explanation Answer: B) 120°

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Q:

A regular hexagonal base prism has height 8 cm and side of base is 4 cm. What is the total surface area (in cm2) of the prism?

A) 54(3 + √3) B) 36(3 + √3)
C) 48(4 + √3) D) 24(4 + √3)
 
Answer & Explanation Answer: C) 48(4 + √3)

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