How many planks each of which is 3 m long,
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 $=6 \mathrm{~m}$

$=6 \times 100 \mathrm{~cm} \quad(\because 1 \mathrm{~m}=100 \mathrm{~cm})$

$=600 \mathrm{~cm}$

Breadth of the block $=75 \mathrm{~cm}$

Height of the block $=45 \mathrm{~cm}$

Volume of block $=$ length $\times$ breadth $\times$ height

$=600 \times 75 \times 45

$=2025000 \mathrm{~cm}^{3}$

Again, it is given that the length of a plank $=3 \mathrm{~m}$

$=3 \times 100 \mathrm{~cm} \quad(\because 1 \mathrm{~m}=100 \mathrm{~cm})$

$=300 \mathrm{~cm}$

Breadth $=15 \mathrm{~cm}$,

Height $=5 \mathrm{~cm}$

Volume of the plank $=$ leng th $\times$ breadth $\times$ height

$=300 \times 15 \times 5=22500 \mathrm{~cm}^{3}$

$\therefore$ The number of such planks $=\frac{\text { volume of the wooden block }}{\text { voume of a plank }}=\frac{2025000 \mathrm{~cm}^{3}}{22500 \mathrm{~cm}^{3}}=90$

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