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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?
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Solution
\[\text { The dimension of the log of wood is 3 m} \times 75 cm \times 50 cm, i . e . , 300 cm \times 75 cm \times 50 cm ( \because 3 m = 100 cm) . \]
\[ \therefore \text { Volume = 300 cm }\times 75 cm \times 50 cm = 1125000 {cm}^3 \]
\[\text { It is given that the side of each cubical block of wood is of 25 cm } . \]
\[\text { Now, volume of one cubical block = (side ) }^3 \]
\[ = {25}^3 \]
\[ = 15625 {cm}^3 \]
\[ \therefore \text { The required number of cubical blocks}= \frac{\text { volume of the wood } \log}{\text { volume of one cubical block }}\]
\[ = \frac{1125000 {cm}^3}{15625 {cm}^3}\]
\[ = 72\]
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