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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 amount of extension in a spring is proportional to the weight hung on it. If the weight of 5 kgs produces an extension of 0.4 cm, what weight would produce an extension of 5cm?

A) 6.25kgs B) 62.5kgs
C) 4kgs D) 40kgs
 
Answer & Explanation Answer: B) 62.5kgs

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Q:

The lengths of two parallel sides of a trapezium are 21 cm and 9 cm. If its height is 10 cm, then what is the area (in cm2) of the trapezium?

A) 35 B) 75
C) 150 D) 225
 
Answer & Explanation Answer: C) 150

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Q:

The whole surface area of a pyramid whose base is a regular polygon is 340 cm2 and area of its base is 100 cm2 . Area of each lateral face is 30 cm2. Then the number of lateral faces is

A) 8 B) 9
C) 7 D) 10
 
Answer & Explanation Answer: A) 8

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Q:

Volume of a cylinder is 2310 cubic cm. If circumference of its base is 44 cm, find the curved surface area of the cylinder?

A) 660 sq cm B) 1320 sq cm
C) 1980 sq cm D) 330 sq cm
 
Answer & Explanation Answer: A) 660 sq cm

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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:

Points P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC. If the ratio of AP:PB is 1:4 and area of Δ APQ is 4 sq cm, what is the area of trapezium PQCB?

A) 60 sq cm B) 16 sq cm
C) 96 sq cm D) 21 sq cm
 
Answer & Explanation Answer: C) 96 sq cm

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Q:

A cone is hollowed out of a solid wooden cube of side 6 cm. The diameter and height of the cone is same as the side of the cube. What is the volume of the remaining cube?

A) 159.42 cubic cms B) 323.15 cubic cms
C) 106.33 cubic cms D) 210.66 cubic cms
 
Answer & Explanation Answer: A) 159.42 cubic cms

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Q:

If triangle ABC = triangle XYZ and angle BAC = 55 deg, then angle ZXY = ?

A) 67.5 deg B) 135 deg
C) 65 deg D) 55 deg
 
Answer & Explanation Answer: D) 55 deg

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