Volume and Surface Areas Questions

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 = units

 

 

II. CUBE 

Let each edge of a cube be of length a. Then,

1. Volume =  cubic units.

2. Surface area = 2(lb +bh +lh) sq.units

3. Diagonal = units

 

 

III. CYLINDER 

Let radius of base = r and Height (or Length) = h. Then, 

1.Volume =  cubic units 

2. Curved surface area =  sq.units

3. Total surface area =  sq.units

 

 

IV. CONE 

Let radius of base =r and Height = h. Then, 

1. Slant height,  units

2. Volume =  cubic units.

3. Curved surface area =  sq.units 

4. Total surface area =  sq.units

 

 

V. SPHERE 

Let the radius of the sphere be r. Then, 

1. Volume = cubic units

2. Surface area =  sq.units

 

 

VI. HEMISPHERE 

Let the radius of a hemisphere be r. Then, 

1. Volume =  cubic units.

2. Curved surface area =  sq.units

3. Total surface area =  sq.units

 

Q:

If each edge of a cube is increased by 50%, find the percentage increase in Its surface area

A) 125% B) 150%
C) 175% D) 110%
 
Answer & Explanation Answer: A) 125%

Explanation:

Let the edge = a cm 

So increase by 50 % =  = 

Total surface Area of original cube = 

TSA of new cube = 

==  

Increase in area =  =

  Increase % = = 125%

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137 27941
Q:

How many cubes of 3cm edge can be cut out of a cube of 18cm edge

A) 36 B) 232
C) 216 D) 484
 
Answer & Explanation Answer: C) 216

Explanation:

number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216

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47 10677
Q:

A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

A) 30 B) 40
C) 10 D) 20
 
Answer & Explanation Answer: B) 40

Explanation:

Volume of the block = (6 x 12 x 15) \inline \fn_jvn cm^3 = 1080 \inline \fn_jvn cm^3

Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm

                                          = 3 cm.

Volume of this cube  = (3 x 3 x 3) \inline \fn_jvn cm^3 = 27 \inline \fn_jvn cm^3

Number of cubes = = 40.

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25 8908
Q:

Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed

A) 486 B) 586
C) 686 D) 786
 
Answer & Explanation Answer: A) 486

Explanation:

Volume of new cube =  

Edge of new cube =  = 9cm

 Surface area of the new cube = ( 6 x 9 x 9)  = 486 

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14 6812
Q:

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

A) 12 pi cub.cm B) 15 pi cub.cm
C) 16 pi cub.cm D) 20 pi cub.cm
 
Answer & Explanation Answer: A) 12 pi cub.cm

Explanation:

ke

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