Question

The outer dimensions of a closed wooden box are $10cm$ by $8cm$ by $7cm$ Thickness of the wood is $2cm$. Find the total cost of wood to make box, if $1c{m}^3$ of wood cost $Rs.2.00$.

Answer 1

The outer dimension of Closed window are $10cm;8cm;7cm$

Thickness of wooden box is $2cm$

The inner dimensions are given by

$10cm-2cm=8cm$

$8cm-2cm=6cm$

$7cm-2cm=5cm$

Therefore, The inner dimensions of wooden box are,

$8cm,6cm,5cm$

Volume of the cuboid $=\text{length}\times \text{breadth}\times \text{height}$

The volume occupied by Wooden box

$=\text{Volume of box with outer dimensions}-\text{Volume of box with inner dimensions}$

$=(10cm\times 8cm\times 7cm)-(8cm\times 6cm\times 5cm)$

$=560c{m}^3-240c{m}^3$

$=320c{m}^3$

Cost of $1c{m}^3$ is $Rs.2.00$

$\Rightarrow$ The total cost $=320\times Rs.2$

$=Rs.640$

Therefore, the total cost of wood to make box is $Rs.640$.