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 Volume and Surface Area Questions

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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 ratio between the vertical angle and a base angle of an isosceles triangle is 4:3. The value of any one base angle is

A) 18 deg B) 54 deg
C) 72 deg D) 10 deg
 
Answer & Explanation Answer: B) 54 deg

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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:

The line passing through (4,3) and (y,0) is parallel to the line passing through (­-1,-­2) and (3,0). Find y?

A) -1 B) -2
C) 2 D) -5
 
Answer & Explanation Answer: B) -2

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Q:

The whole surface area of a pyramid whose base is a regular polygon is 340 cm2 and area of its base is 100 cm2 . Area of each lateral face is 30 cm2. Then the number of lateral faces is

A) 8 B) 9
C) 7 D) 10
 
Answer & Explanation Answer: A) 8

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Q:

In a rectangle

A) Diagonals bisect opposite angles B) Consecutive sides are congruent
C) All sides are congruent D) Diagonals form two congruent triangles
 
Answer & Explanation Answer: D) Diagonals form two congruent triangles

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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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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 , -1) and (3 , 5) respectively?

A) (-3 , 8) B) (3 , 8)
C) (-3 , -8) D) (3 , -8)
 
Answer & Explanation Answer: A) (-3 , 8)

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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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