Question

How many planks each of which is 3 m long, 15 cm broad and 5 cm thick can be prepared from a 6 m long, 75 cm broad and 45 cm thick wooden block?
A) 90
B) 85
C) 56
D) 12

Answer 1

Hint: We will make use of the fact that the volume of the given one wooden block and the number of planks possible to be made must be the same and then by equating those by using their formula, we will get the number of planks.

Complete step-by-step answer:
We know that the volume of a cuboid is given by the following formula:-
$ \Rightarrow Volume = l \times b \times h$, where l is the length, b is the breadth and h is the height of the cuboid.
We will convert every unit from m to cm to make everything into cm only.
We know that: 1 m = 100 cm.
Therefore, the length of plank = 3 m = 300 cm.
Length of the wooden block = 600 cm.
Now, let us first find the volume of the plank.
$ \Rightarrow Volume = (300 \times 15 \times 5)c{m^3}$
On simplifying the calculations on the RHS, we will get the following calculations:
$ \Rightarrow Volume = 22500c{m^3}$
Now, let us find the volume of the wooden block.
$ \Rightarrow Volume = (600 \times 75 \times 45)c{m^3}$
On simplifying the calculations on the RHS, we will get the following calculations:
$ \Rightarrow Volume = 2025000c{m^3}$
Let us assume that we can form n number of planks out of it.
Therefore, the volume of wooden block and the n wooden planks must be equal.
$\therefore 2025000c{m^3} = n \times 22500c{m^3}$
Rearranging the terms to get the following expression:-
$\therefore n = \dfrac{{2025000}}{{22500}}$
On simplifying the calculations on the RHS:-
$ \Rightarrow n = 90$
$\therefore $ we can make 90 planks out of the wooden block.

$\therefore $ The correct option is (A).

Note: The students must note that we have basically used the wooden block only to convert into the wooden planks. Therefore, the volume of wooden blocks must definitely be equal to the volume of however wooden planks we created out of it. Because the amount of wood must be the same.