Volume and Surface Area Questions

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:

ΔABC is right angled at B. BD is the altitude. AD is 8 cm and DC is 50 cm. What is the length of BD?

A) 25 cm B) 20 cm
C) 16 cm D) 15 cm
 
Answer & Explanation Answer: B) 20 cm

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Q:

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:3, what is the ratio of area of ΔADE and area of quadrilateral BDEC?

A) 4 : 21 B) 4 : 25
C) 4 : 29 D) 4 : 9
 
Answer & Explanation Answer: A) 4 : 21

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Q:

What is the reflection of the point (-1 , 3) in the line x = -4?

A) (-7 ,-3) B) (-7 ,3)
C) (7 ,-3) D) (7 ,3)
 
Answer & Explanation Answer: B) (-7 ,3)

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Q:

Δ DEF is right angled at E. If m∠F = 45°, then what is the value of 2 Sin F x Cot F?

A) √2 B) 2
C) 1/√2 D) 1/2
 
Answer & Explanation Answer: A) √2

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Q:

AD is the Median of Δ ABC. If O is the centroid and AO = 10 cm then OD is

A) 5 cm B) 20 cm
C) 10 cm D) 30 cm
 
Answer & Explanation Answer: A) 5 cm

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Q:

A cylindrical vessel of height 7 cm and radius 5 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius 8 cm what will be the height of this cone?

A) 8.2 cm B) 16.4 cm
C) 24.6 cm D) 32.8 cm
 
Answer & Explanation Answer: A) 8.2 cm

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Q:

If the lengths of the two parallel sides of a trapezium are 8 cm and 10 cm and its area is 54 cm². Find the distance between its parallel sides (in cm).

A) 6 B) 3
C) 12 D) 9
 
Answer & Explanation Answer: A) 6

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Q:

What is the area (in square units) of the figure enclosed by the graphs of the lines x = -4, x =2, y = -2 and y = 3?

A) 12 B) 24
C) 15 D) 60
 
Answer & Explanation Answer: C) 15

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