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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 the side AB of an equilateral triangle ABC is equal to 12 cm. Calculate the length( in cm) of the AO, if O is the centroid of the triangle.

A) 2√3 B) 3√3
C) 4√3 D) 9√3
 
Answer & Explanation Answer: C) 4√3

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Q:

What is the equation of the line perpendicular to the line 2x + 3y= -6 and having Y-intercept 3?

A) 3x - 2y = 6 B) 3x - 2y = -6
C) 2x - 3y = -6 D) 2x - 3y = 6
 
Answer & Explanation Answer: B) 3x - 2y = -6

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Q:

 In ΔDEF measure of angle E is 90 deg. If tanD = 4/3, and DE = 6cm, then what is the length (in cm) of side EF?

A) 10 B) 5
C) 8 D) 4
 
Answer & Explanation Answer: C) 8

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Q:

Suppose that the medians BD, CE and AF of a triangle ABC meet at G. Then AG: GF is

A) 1:2 B) 2:1
C) 1:3 D) 2:3
 
Answer & Explanation Answer: B) 2:1

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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 = 2:5 and area of ΔADE is 8 sq cm, what is the ratio of area of ΔADE: area of quadrilateral BDEC?

A) (4:45) B) (45:4)
C) (8:45) D) (45:8)
 
Answer & Explanation Answer: A) (4:45)

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Q:

If the sum of radius and height of a solid cylinder is 20 cm and its total surface area is 880 cm then its volume is

A) 1760 cm3 B) 8800 cm3
C) 2002 cm3 D) 4804 cm3
 
Answer & Explanation Answer: C) 2002 cm3

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Q:

The height and the total surface area of a right circular cylinder are 4 cm and 8π sq.cm. respectively. The radius of the base of cylinder is

A) (2√2 - 2) cm B) (2 - √2) cm
C) 2 cm D) √2 cm
 
Answer & Explanation Answer: A) (2√2 - 2) cm

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Q:

Analyze the figure shown below in which DE || BC and the other dimensions are as follows: AD=3 cm, BD=4 cm, AE=4.4 cm and DE=6 cm. Calculate the length (in cm) of BC.

A) 6 B) 8
C) 12 D) 14
 
Answer & Explanation Answer: D) 14

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