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How many planks each of which is $3 m$ long, $15 cm$ broad and 5 cm thick can be prepared from a wooden block 6 m long, $75 cm$ broad and $45 cm$ thick?

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answer is B.

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Detailed Solution

It is given planks of dimensions 3 m length, 15 cm breadth and 5 cm thickness and a wooden block of 6 m length, 75 cm breadth and 45 cm thickness.
Converting the length of one plank from 3

m

to equivalent cm using

1 m = 1 × 100 c m

⇒ 3 m = 3 × 100 c m ⇒ 3 m = 300 c m

Convert the length of wooden block from

6 m

to equivalent cm using

1 m = 1 × 100 c m

⇒ 6 m = 6 × 100 c m ⇒ 6 m = 600 c m

We know that, the formula for calculating the volume of the cuboid is given by:

V = l × b × h

where

l

b

and

h

are the length, breadth, and height of cuboids.
Computing the volume of the wooden block by substituting

l = 600

b = 75

and

h = 45

into the formula.
The volume of the wooden block =

600 c m × 75 c m × 45 c m

Computing the volume of the one plank by substituting

l = 300

b = 15

and

h = 5

into the formula.
The volume of the one plank =

300 c m × 15 c m × 5 c m

.
Determining the number of planks by dividing the volume of the wooden blocks by the volume of one plank,

N u m b e r o f p l a n k s = 600 c m × 75 c m × 45 c m 300 c m × 15 c m × 5 c m

⇒ N u m b e r o f p l a n k s = 2 × 5 × 9 ⇒ N u m b e r o f p l a n k s = 90

Thus, the number of planks that can be prepared are 90.
Hence option (2) is correct.

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