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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:

In ΔABC, the medians AD and BE meet at G. The ratio of the areas of ΔBDG and the quadrilateral GDCE is

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

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0 1385
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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0 1385
Q:

The midpoints of AB and AC of a triangle ABC are X and Y respectively. If BC+XY=12 units, then BC­XY is

A) 10 units B) 8 units
C) 6 units D) 4 units
 
Answer & Explanation Answer: D) 4 units

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0 1381
Q:

If O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O, a point P is taken. From this point, two tangents PQ and PR are drawn to the circle. Then , the area of quadrilateral PQOR is

A) 60 cm2 B) 32.5 cm2
C) 65 cm2 D) 30 cm2
 
Answer & Explanation Answer: A) 60 cm2

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0 1380
Q:

Find the volume (in cub.cm) of a hemisphere of diameter 21 cm.

A) 2235.5 B) 2425.5
C) 2040 D) 1860
 
Answer & Explanation Answer: B) 2425.5

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0 1379
Q:

The lengths of diagonals of a rhombus are 24cm and 10cm the perimeter of the rhombus (in cm ) is :

A) 52 B) 56
C) 68 D) 72
 
Answer & Explanation Answer: A) 52

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0 1379
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:

A regular pyramid has a square base. The height of the pyramid is 22 cm and side of its base is 14 cm. Volume of pyramid is equal to the volume of a sphere. What is the radius (in cm) of the sphere?

A) 493 B) 7
C) 14 D) 983
 
Answer & Explanation Answer: B) 7

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