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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 diagonals do not form at least two congruent triangles in a _____.

A) Parallelogram B) Rhombus
C) Trapezium D) Kite
 
Answer & Explanation Answer: C) Trapezium

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Q:

A cylinder of radius 4.5 cm and height 12 cm just fits in another cylinder completely with their axis perpendicular. What is the radius (in cm) of second cylinder?

A) 5 B) 6
C) 15 D) 7.5
 
Answer & Explanation Answer: D) 7.5

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Q:

In the given figure, PQ is the diameter of the circle. What is the measure (in degrees) of QSR?

A) 23 B) 37
C) 47 D) 57
 
Answer & Explanation Answer: C) 47

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Q:

PQR is an equilateral triangle. MN is drawn parallel to QR such that M is on PQ and N is on PR. If PN = 6 cm, then the length of MN is

A) 3 cm B) 6 cm
C) 12 cm D) 4.5 cm
 
Answer & Explanation Answer: B) 6 cm

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Q:

A solid sphere of radius 9 cm is melted to form a sphere of radius 6 cm and a right circular cylinder of same radius. The height of the cylinder so formed is

A) 19 cm B) 21 cm
C) 23 cm D) 25 cm
 
Answer & Explanation Answer: A) 19 cm

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Q:

The base of a right prism is a trapezium whose the length of parallel sides are 25 cm and 11 cm and the perpendicular distance between the parallell sides in 16 cm. If the height of the prism is 10 cm, then the volume of the prism is

A) 1440 cu.cm B) 1540 cu.cm
C) 2880 cu.cm D) 960 cu.cm
 
Answer & Explanation Answer: C) 2880 cu.cm

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Q:

At what point does the line 2x - 3y = 6 cuts the Y axis?

A) (0, 2) B) (-2, 0)
C) (2, 0) D) (0, -2)
 
Answer & Explanation Answer: D) (0, -2)

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Q:

In the given figure, P  is the center of the circle. If QS = PR, then what is the ratio of angles RSP to the TPR ?

A) 1 : 4 B) 2 : 5
C) 1 : 3 D) 2 : 7
 
Answer & Explanation Answer: C) 1 : 3

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