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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:

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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0 1211
Q:

If 4r = h + r2+h2  then r: h = ? (r not equal to 0)

A) 17:8 B) 8:17
C) 8:15 D) 15:8
 
Answer & Explanation Answer: C) 8:15

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1 1210
Q:

If a cone of radius 3.5 cm and height 9.6 cm is melted and constructed into a cylinder of the same radius, what will be the height of this cylinder? (Take π = 22/7)

A) 3.2 cm B) 6.4 cm
C) 1.6 cm D) 4.8 cm
 
Answer & Explanation Answer: A) 3.2 cm

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1 1208
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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0 1207
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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1 1205
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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0 1202
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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0 1202
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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1 1198