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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 7 cm is partially filled with water. By how much will the water level rise if a sphere of radius 6 cm is completely immersed in this water?

A) 11.76 cm B) 17.64 cm
C) 23.52 cm D) 5.88 cm
 
Answer & Explanation Answer: D) 5.88 cm

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Q:

The volume of a hemisphere is 19404 cm3. Find its diameter (in cm).

A) 42 B) 21
C) 84 D) 63
 
Answer & Explanation Answer: A) 42

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Q:

What are the co-ordinates of the centroid of a triangle, whose vertices are A(2 , 5), B(-4 , 0) and C(5 , 4)?

A) (-1 , 3) B) (1 , 3)
C) (1 , -3) D) (-1 , -3)
 
Answer & Explanation Answer: B) (1 , 3)

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Q:

ΔABC is isosceles having AB = AC and ∠A = 40°. Bisectors PO and OQ of the exterior angles ∠ABD and ∠ACE formed by producing BC on both sides, meet at O. Then the value of ∠BOC is

A) 70° B) 110°
C) 80° D) 55°
 
Answer & Explanation Answer: A) 70°

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Q:

What is the slope of the line perpendicular to the line passing through the points (­6,3) and (2,7)?

A) -2 B) 2
C) 1/2 D) -1/2
 
Answer & Explanation Answer: A) -2

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Q:

A triangle is circumscribed on the circle of centre O in such a way that sides AB = 12 cm, BQ = 7 cm and CQ = 5 cm. Calculate the lengtth (in cm) of side AC.

A) 8 B) 10
C) 12 D) 14
 
Answer & Explanation Answer: B) 10

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Q:

If a regular polygon has 10 sides then the measure of its interior angle is greater than the measure of its exterior angle by how many degrees?

A) 120 B) 132
C) 140 D) 108
 
Answer & Explanation Answer: D) 108

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Q:

The area and the length of one of the diagonals of a rhombus is 60 cm2 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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