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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:

AB is a chord of the circle and its center is “O”. ON is perpendicular to AB. If the length of AB=20 cm, ON-(2√11) cm, find the radius (in cm) of the circle.

A) 10 B) 12
C) 13 D) 15
 
Answer & Explanation Answer: B) 12

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Q:

AB is a chord of the circle and its center is “O”. ON is perpendicular to AB. If the length of AB=20 cm, ON-(2√11) cm, find the radius (in cm) of the circle.

A) 10 B) 12
C) 13 D) 15
 
Answer & Explanation Answer: B) 12

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Q:

The sum of radii of the two circles is 91 cm and the difference between their area is 2002 cm2 . What is the radius (in cm) of the larger circle?

A) 56 B) 42
C) 63 D) 49
 
Answer & Explanation Answer: D) 49

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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:

Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 6 cm, then what is the area (in sq.cm) of an equilateral triangle whose side is equal to the bigger diagonal of the rhombus?

A) 18√3 B) 27√3
C) 32√3 D) 36√3
 
Answer & Explanation Answer: B) 27√3

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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:

If in ΔABC, DE ||BC, AB = 7.5cm, BD = 6cm and DE = 2cm, then the length of BC in cm is

A) 6 B) 8
C) 10 D) 10.5
 
Answer & Explanation Answer: C) 10

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Q:

If the volume of a cylinder is 385 cubic cm and height is 10 cm, find its radius?

A) 7 cm B) 10.5 cm
C) 3.5 cm D) 1.75 cm
 
Answer & Explanation Answer: C) 3.5 cm

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