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Question
How many planks each of which is 3 m long, 15 cm broad and 5 cm thick can be prepared from a wooden block 6 m long, 75 cm broad and 45 cm thick?
Solution
Length of the wooden block = 6 m
\[ = 6 \times 100 cm ( \because 1 m = 100 cm)\]
= 600 cm
Breadth of the block = 75 cm
Height of the block = 45 cm
\[\text { Volume of block = length } \times \text { breadth } \times \text { height }\]
\[ = 600 \times 75 \times 45\]
\[ = 2025000 {cm}^3 \]
Again, it is given that the length of a plank = 3 m
\[ = 3 \times 100 cm ( \because 1 m = 100 cm)\]
= 300 cm
Breadth = 15 cm,
Height = 5 cm
\[\text { Volume of the plank = length } \times\text { breadth } \times \text { height }\]
\[ = 300 \times 15 \times 5 = 22500 {cm}^3 \]
\[ \therefore\text { The number of such planks } = \frac{\text { volume of the wooden block }}{\text { voume of a plank }} = \frac{2025000 {cm}^3}{22500 {cm}^3} = 90\]
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