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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:

Point A (2, 1) divides segment BC in the ratio 2:3. Co-ordinates of B are (1, -3) and C are (4, y). What is the value of y?

A) 8 B) -7
C) -8 D) 7
 
Answer & Explanation Answer: D) 7

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Q:

The line parallel to the BC of the triangle ABC divides the other two sides at the point D and E in such a way that AB=3AD. Calculate the ratio of DE and BC.

 

A) 1:6 B) 1:4
C) 1:3 D) 3:1
 
Answer & Explanation Answer: C) 1:3

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Q:

In which of the following quadrilaterals only one pair of opposite angles is supplementary?

A) Isosceles Trapezium B) Parallelogram
C) Cyclic quadrilateral D) Rectangle
 
Answer & Explanation Answer: C) Cyclic quadrilateral

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Q:

A solid right circular cone of radius 10 cm and height 8 cm is put inside a cylindrical vessel of radius 11 cm and height 9 cm. How much water in cubic cm will be required to fill the cylindrical vessel completely?

A) 5168.96 cubic cms B) 2584.48 cubic cms
C) 7753.44 cubic cms D) 1292.24 cubic cms
 
Answer & Explanation Answer: B) 2584.48 cubic cms

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Q:

If the curved surface area of a right circular cone is 10010 sq cm and its slant height is 91 cm, find its total surface area.

A) 27720 sq cm B) 4620 sq cm
C) 6930 sq cm D) 13860 sq cm
 
Answer & Explanation Answer: D) 13860 sq cm

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Q:

O is an centre of a circle. P is an external point of it at distance of 13cm from O. The radius of the circle is 5cm. Then the length of a tangent to the circle from P upto the point of contact is

A) √194cm B) 10cm
C) 12cm D) 8cm
 
Answer & Explanation Answer: C) 12cm

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Q:

Find the volume (in cm3) of a cuboid of length, breadth and height of 8.5 cm, 6 cm and 7 cm respectively.

A) 524 B) 626
C) 603 D) 357
 
Answer & Explanation Answer: D) 357

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Q:

The point of the intersection of three medians is known as the ____________.

A) circum-centre B) in-center
C) centroid D) orthocenter
 
Answer & Explanation Answer: C) centroid

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