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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:

The ratio of curved surface area of a right circular cylinder to the total area of its two bases is 2 : 1. If the total surface area of cylinder is 23100 cm2, then what is the volume (in cm3) of cylinder?

A) 247200 B) 269500
C) 312500 D) 341800
 
Answer & Explanation Answer: B) 269500

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Q:

PQ is a diameter of a circle with centre O. RS is a chord parallel to PQ subtends an angle of 40° at the centre of the circle. If PR and QS are produced to meet at T, then what will be the measure (in degrees) of ∠PTQ?

A) 55 B) 60
C) 70 D) 90
 
Answer & Explanation Answer: C) 70

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Q:

Find length of the arc whose central angle is 90° and radius of the circle is 3.5 cm?

A) 11 cm B) 5.5 cm
C) 16.5 cm D) 22 cm
 
Answer & Explanation Answer: B) 5.5 cm

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Q:

What is the reflection of the point (5 , -1) in the line y = 2?

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

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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:

O is the centre of the circle and ∠AOB = 150°, and the shaded portion is x part of the circular region, then x = ?

A) 1/12 B) 1/9
C) 1/6 D) 1/4
 
Answer & Explanation Answer: C) 1/6

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Q:

The length, breadth and height of a cuboid are 12 cm, 8 cm and 6 cm respectively. The volume of the cuboid is (Use π = 22/7)

A) 1152 cubic cms B) 288 cubic cms
C) 576 cubic cms D) 864 cubic cms
 
Answer & Explanation Answer: C) 576 cubic cms

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Q:

In the given fig, ST||RP, then what is the value of supplementary angle y (in deg)?

A) 10 B) 60
C) 100 D) 170
 
Answer & Explanation Answer: C) 100

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