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An $8 m$ long cuboidal beam of wood when sliced produces four thousand $1 cm$ cubes and there is no wastage of wood in this process. If one edge of the beam is $0.5 m$ ,find the third edge.

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0.001 m

0.004 m

0.012 m

0.023 m

answer is A.

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Detailed Solution

Given, two of the dimensions of cuboidal beam are 8m and 0.5m. Edge of cube=1cm
Number of cubes=4000
The formula for calculating the volume of a cube is given by,

V = a 3

…... (1)
Here,

a

is the side of a cube.
The formula for calculating the volume of the cuboid is given by,

V = l × b × h

…... (2)
Here,

l

b

and

h

are the length, breadth, and height of cuboids.
The formula for converting the value in cm to the meter is given by,

1 c m = 1100 m

Let h be the third edge of the beam.
Convert the edge of each cube 1 cm into meters using the formula

⇒ 1 c m = 1100 m ⇒ 1 c m = 0.01 m

Computing the volume of the beam by substituting

a = 0.01

into the formula

1

.
Volume of 1 beam =

0.01 3

m 3

.
Computing the volume of 4000 cubical sliced beam by multiplying the volume of one beam to 4000.
Volume of 4000 cubical sliced =

4000 (0.01) 3 m 3

⇒ V o l u m e o f 4000 c u b i c a l s l i c e d = 0.004 m 3

Substitute

l = 8 m

b = 0.5 m

and V=0.004

m 3

into the formula

2

0.004 m 3 = 8 m × 0.5 m × h

Computing the value of

h

by simplifying the expression.

⇒ h = 0.004 m 3 8 m × 0.5 m ⇒ h = 0.001 m

Thus, the third edge is

0.001 m

.
Hence option (1) is correct.

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