Question

A closed rectangular box is made of wood of 1.5 cm thickness .the exterior length and breadth are respectively 78 cm and 19 cm ,and the capacity of the box is 5 cubic decimetres . calculate the exterior height of the box .
i want step-wise explanations

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{A closed rectangular box is made of wood of 1.5 cm thickness}$

$\textsf{The exterior length and breadth are respectively 78 cm}$

$\textsf{and 19 cm ,and the capacity of the box is 5 cubic decimetres}$

$\underline{\textbf{To find:}}$

$\textsf{Exterior height of the box}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Formula used:}}$

$\boxed{\mathsf{Volume\;of\;cuboid=l{\times}b{\times}h\;cubic\;units}}$

$\textsf{Let h be the exterior height of the rectangular box}$

$\mathsf{Then,}$

$\textsf{Interior length of the box=78-2(1.5)=78-3=75 cm}$

$\textsf{Interior breadth of the box=19-2(1.5)=19-3=16 cm}$

$\textsf{Interior height of the box=h-2(1.5)=h-3 cm}$

$\textsf{Now,}$

$\mathsf{Capacity\;of\;the\;box=5\;dm^3=5000\;cm^3}$

$\implies\mathsf{75{\times}16{\times}(h-3)=5000}$

$\implies\mathsf{h-3=\dfrac{5000}{75{\times}16}}$

$\implies\mathsf{h-3=4.17}$

$\implies\mathsf{h=4.17+3}$

$\implies\boxed{\mathsf{h=7.17\;cm}}$

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