Question

The number of wooden cubical blocks of edge 20cm that can be cut out from another cubical block of the wood of edge 3m 60cm is
A) 5382
B) 5832
C) 5283
D) None of these

Answer 1

Hint: In this question first convert the length of the large cube in centimetre then calculate the volume of both large and small cube after that divide volume of the large cube to volume of each small block to get the number of the small wooden cube which can be cut from the larger cube.

Complete step by step solution: Given edge of large cubical wooden block $ = 3m\;60cm$
Convert length of edge in centimeter,
i.e.$3m\;60cm$= $3 \times 100 + 60 = 360$\[ = \]360cm (since 1m is 100cm)
Volume of a large cube\[ = {\text{edge}^3}\]
     \[ = {{360}^3}\]
     $ = 360 \times 360 \times 360$
     \[ = \]46656000\[c{m^3}\]
$ \Rightarrow $ Volume of a large cube is 46656000 \[c{m^3}\]
Given edge of small cubical wooden block =20cm
Volume of a small cube \[ = {(edge)^3}\]
     \[ = {(20)^3}\]
     $ = 20 \times 20 \times 20$
     \[ = 8000c{m^3}\]
$ \Rightarrow $ Volume of a small cube is \[8000c{m^3}\]
Let the number of small cubical wooden block of edge 20cm is N
$ \Rightarrow $N$ = $$\dfrac{{{\text{volume of large cube}}}}{{{\text{volume of each small cube}}}}$
$ \Rightarrow $N$ = \dfrac{{46656000}}{{8000}}$
\[ \Rightarrow N = \dfrac{{46656}}{8}\]
$ \Rightarrow $N$ = 5832$
Thus, the total number of the small cubical wooden block can form large cubical wooden block is 5832.
Hence, Option B. 5832 is the correct answer.



Note: In this type of question one should always check the units of the length it should be always in one unit only. Either in centimetre or meter. If not then before solving the question first do the conversion and then proceed further.