How many wooden cubical blocks of side 25 cm can be cut from a log of wood of size 3 m by 75 cm by 50 cm,
Question:

How many wooden cubical blocks of side 25 cm can be cut from a log of wood of size 3 m by 75 cm by 50 cm, assuming that there is no wastage?

Solution:

The dimension of the $\log$ of wood is $3 \mathrm{~m} \times 75 \mathrm{~cm} \times 50 \mathrm{~cm}$, i. e., $300 \mathrm{~cm} \times 75 \mathrm{~cm} \times 50 \mathrm{~cm}(\because 3 \mathrm{~m}=100 \mathrm{~cm})$.

$\therefore$ Volume $=300 \mathrm{~cm} \times 75 \mathrm{~cm} \times 50 \mathrm{~cm}=1125000 \mathrm{~cm}^{3}$

It is given that the side of each cubical block of wood is of $25 \mathrm{~cm}$.

Now, volume of one cubical block $=(\text { side })^{3}$

$=25^{3}$

$=15625 \mathrm{~cm}^{3}$

$\therefore$ The required number of cubical blocks $=\frac{\text { volume of the wood log }}{\text { volume of one cubical block }}$

$=\frac{1125000 \mathrm{~cm}^{3}}{15625 \mathrm{~cm}^{3}}$

$=72$

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