Question

How many planks each of which is $2m$ long, $2.5cm$broad and $4cm$ thick can be cut-off from a wooden block $6m$long, $15cm$ broad and $40cm$ thick?

Answer 1

Hint- In this question dimensions of wooden block and dimensions of single plank is given , so in order to find the total number of planks we will simply calculate it by dividing volume of wooden block by volume of single plank therefore at first we will find the volume of wooden block and volume of single plank.

Complete step-by-step answer:
Given that length of wooden block
$\because (1m = 100cm)$
$ 6m= 600cm$
Breadth of wooden block $ = 15cm$
Height of wooden block $ = 40cm$
Length of single plank $ = (\therefore 1m = 100cm)$
$2m = 200cm$
Breadth of single plank $ = 2.5cm$
Height of single plank $ = 4cm$
Now we will evaluate volume of single plank as well as wooden block
As we know that volume of cuboid is given as
Volume of cuboid = length $ \times $ breadth $ \times $ height of cuboid
Here wooden block and plank consist same shape as cuboid
Therefore volume of wooden block = length $ \times $ breadth $ \times $ height of wooden block
Substitute given values in above formula we have
$ = 600 \times 15 \times 40 = 360000c{m^3}$
Similarly, volume of 1 plank = length $ \times $ breadth $ \times $ height of single plank
Substitute given values in above formula we have
$ = 200 \times 2.5 \times 4 = 2000c{m^3}$
Thus, number of planks that can be cut off from block = Number of wooden block $/$volume of each planks
By substituting obtained values in above formula we have
$ = 360000/2000 = 180$
Hence, the required number of planks is $180$.

Note- We have to learn the scale $3$ sides to determine the volumes. It is expressed in cubic units, since volume includes $3$ sides. Cubic units volume $ = $ length $ \times $width $ \times $ height $ = (l \times b \times h)$. Where
$l$ is the length of the cuboid, $b$ is the breath of the cuboid and $h$is the height of the cuboid.