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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 a triangle the length of the side opposite the angle which measures 45° is 8 cm, what is the length of the side opposite to the angle which measures 90°?

A) 8√2 cm B) 4√2 cm
C) 8√3 cm D) 4√3 cm
 
Answer & Explanation Answer: A) 8√2 cm

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Q:

A chord of a circle is equal to its radius. A tangent is drawn to the circle at an extremity of the chord. The angle between the tangent and the chord is

A) 30° B) 45°
C) 60° D) 75°
 
Answer & Explanation Answer: A) 30°

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Q:

The curved surface area and the diameter of a right circular cylinder are 352 cm² and 14 cm respectively. Find its height (in cm).

A) 9 B) 8
C) 10 D) 11
 
Answer & Explanation Answer: B) 8

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Q:

In a triangle the length of the side opposite the angle which measures 30° is 9 cm, what is the length of the side opposite to the angle which measures 60°?

A) 3√3 cm B) 3/2 cm
C) 9/2 cm D) 9√3 cm
 
Answer & Explanation Answer: D) 9√3 cm

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Q:

O is an centre of a circle. P is an external point of it at distance of 13cm from O. The radius of the circle is 5cm. Then the length of a tangent to the circle from P upto the point of contact is

A) √194cm B) 10cm
C) 12cm D) 8cm
 
Answer & Explanation Answer: C) 12cm

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Q:

Possible length of the three sides of a triangle are :­

A) 2 cm , 3 cm , 6 cm B) 3 cm , 4 cm , 5 cm
C) 2.5 cm , 3.5 cm , 6 cm D) 4 cm , 4 cm , 9 cm
 
Answer & Explanation Answer: B) 3 cm , 4 cm , 5 cm

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Q:

A prism has a regular hexagonal base with side 6 cm. If the total surface area of prism is 216√3 cm2, then what is the height (in cm) of prism?

A) 3√3 B)  6√3
C) 6 D) 3
 
Answer & Explanation Answer: A) 3√3

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Q:

The co-ordinates of the centroid of a triangle ABC are (2 , 2). What are the co-ordinates of vertex C if co-ordinates of A and B are (7 , -1) and (1 , 2) respectively?

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

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