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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 right circular cylinder is formed. A = sum of total surface area and the area of the two bases. B = the curved surface area of this cylinder. If A : B = 3 : 2 and the volume of cylinder is 4312 cm3, then what is the sum of area (in cm2) of the two bases of this cylinder?

A) 154 B) 308
C) 462 D) 616
 
Answer & Explanation Answer: B) 308

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0 1223
Q:

PQRS is a cyclic quadrilateral and PQ is the diameter of the circle. If ∠RPQ = 38°, then what is the value (in degrees) of ∠PSR?

A) 52 B) 77
C) 128 D) 142
 
Answer & Explanation Answer: C) 128

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0 1223
Q:

In the figure, a circle touches quadrilateral ABCD. If AB = 2x + 3, BC = 3x - 1, CD = x + 6 and DA = x + 4, then what is the value of x?

A) 3 B) 4.5
C) 6 D) 6.5
 
Answer & Explanation Answer: C) 6

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1 1219
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 1215
Q:

In ΔABC , DE || AC. Where D and E are two points lying on AB and BC respectively. If AB = 5 cm and AD = 3 cm, then BE : EC is

A) 2:3 B) 3:2
C) 5:3 D) 3:5
 
Answer & Explanation Answer: A) 2:3

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0 1214
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 1203
Q:

If curved surface area of a cylinder is 1386 sq cm and height is 21 cm, what will be its radius? (Take π = 22/7)

A) 21 cms B) 5.25 cms
C) 10.5 cms D) 15.75 cms
 
Answer & Explanation Answer: C) 10.5 cms

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1 1194
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 1194