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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:

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:

Two circles touch each other at point X. Two common tangents of the circles meet at point P and none of the tangents passes through X. These tangents touch the larger circle at points B and C. If the radius of the larger circle is 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?

A) 3.5 B) 3.75
C) 4.25 D) 4.45
 
Answer & Explanation Answer: B) 3.75

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Q:

The perimeter and the breadth of a rectangle are 44 cm and 10 cm respectively. Find its area (in cm2).

A) 60 B) 240
C) 120 D) 180
 
Answer & Explanation Answer: C) 120

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Q:

Which one of the following combination of measurements can form the sides of a triangle?

A) 9 cm, 6 cm, 2 cm B) 11 cm, 3 cm, 12 cm
C) 3 cm, 5 cm, 8 cm D) 5 cm, 7 cm, 13 cm
 
Answer & Explanation Answer: B) 11 cm, 3 cm, 12 cm

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Q:

Curved surface area of a cylinder is 440 sq cm. If circumference of its base is 44 cm, what is the volume of the cylinder? (Take π = 22/7)

A) 1540 cubic cm B) 3080 cubic cm
C) 770 cubic cm D) 2310 cubic cm
 
Answer & Explanation Answer: A) 1540 cubic cm

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Q:

The curved surface area of a hemisphere is 27.72 sq cm and volume is 19.404 cubic cm, find its radius?

A) 4.2 cm B) 2.1 cm
C) 0.7 cm D) 1.05 cm
 
Answer & Explanation Answer: B) 2.1 cm

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Q:

What is the total surface area (in sq cm) of a hollow cylinder open at both ends, if its length is 22 cm, external radius is 7 cm and thickness is 1 cm? (Take π = 22/7)

A) 1879.43 B) 3758.86
C) 939.715 D) 2819.145
 
Answer & Explanation Answer: A) 1879.43

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Q:

What is the reflection of the point (-3, 1) in the line x = -2?

A) (-1 , 1) B) (-3 , -5)
C) (1 , 1) D) (-3 , 5)
 
Answer & Explanation Answer: A) (-1 , 1)

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