Volume and Surface Area Questions

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:

The total surface area of a cube is 73.5 sq.cm. Find its side (in cm).

A) 3.5 B) 4.5
C) 7.5 D) 5.5
 
Answer & Explanation Answer: A) 3.5

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Q:

In a triangle ABC, ∠A = 70°, ∠B = 80° and D is the incentre of ΔABC. ∠ACB = 2x° and ∠BDC = y°. The values of x and y, respectively are

A) 15, 130 B) 15, 125
C) 35, 40 D) 30, 150
 
Answer & Explanation Answer: B) 15, 125

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Q:

In the two triangles ABC and DEF the sides AB = DE and BC = EF. Which of the following option is correct which results in the ABC DEF?

 

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

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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:

The co-ordinates of the centroid of a triangle ABC are (1 , -4). What are the co-ordinates of vertex C if co-ordinates of A and B are (3 , -4) and (0 , 5) respectively?

A) (0 , 13) B) (0, 5)
C) (0, -5) D) (0 , -13)
 
Answer & Explanation Answer: D) (0 , -13)

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Q:

In the circle above, chord AB is extended to meet the tangent DE at D. If AB = 5 cm and DE = 6 cm, find the length of BD.

 

A) 4 cm B) 5 cm
C) 6 cm D) √30 cm
 
Answer & Explanation Answer: A) 4 cm

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Q:

The length of one side of a rhombus is 41 cm and its area is 720 sq.cm. What is the sum of the lengths of its diagonals?

A) 82 cm B) 90 cm
C) 98 cm D) 80 cm
 
Answer & Explanation Answer: C) 98 cm

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Q:

In a triangle, the length of the side opposite the angle which measures 45° is 16 cm, what is the length of the side opposite to the angle which measures 90°? 

A) 8√3 cm B) 16√2 cm
C) 8 cm D) 16√3 cm
 
Answer & Explanation Answer: B) 16√2 cm

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