Question

7.
A metal cuboid has dimensions 4 cm x 6cm x 10 cm. If the maximum pressure it can
exert on a flat surface is 8000 Pa what is the minimum pressure it will exert?

Answer 1

$\huge\boxed{\mathbf\green{Solution :-}}$

$\large\underline\mathbf\purple{⚘\:Given :-}$

$\small\mathbf{◑\:A\:metal\:cuboid\:of\:dimention}\\{\mathbf{4cm×6cm×10cm}}$

$\large\underline\mathbf\blue{⚘\:To\:Find :-}$

$\small\mathbf{◑\: Minimum\: pressure\: exerted\:by\:the\:cuboid}$

$\large\underline\mathbf\blue{⚘\:Solving :-}$

$\small\implies\mathbf{we\:know\; that:-}$

$\small\mathbf{†\:\:\:\:P=\frac{F}{A}}$

$\small\mathbf{where,}$

$\small\mathbf{◑\:P = Pressure}$

$\small\mathbf{◑\:F=Force}$

$\small\mathbf{◑\:A=Area}$

$\small\mathbf{\underline{we\:know\:that:-}}$

$\small\mathbf\blue{☯\:Smaller\:the\:area\:greater\:the\:force}$

$\small\mathbf{And}$

$\small\mathbf\blue{☯\:Larger\:the\:area\:lesser\:the\:force}$

$\small\mathbf{so,}$

$\small\mathbf{For\: Maximum\: pressure\:area=4cm×6cm=24cm²}$

$\small\mathbf{\therefore{A=24cm²}}$

$\small\mathbf{\underline{Now,\: putting\: the\:value\:in\:the\: equation:-}}$

$\small\implies\mathbf{8000\:Pa=\frac{F}{24cm²}}$

$\small\mathbf{∴\:F=8000\:Pa×24cm²}$

$\small\boxed{\mathbf\green{Now,\:claculating\: minimum\:area:-}}$

$\small\mathbf{\: minimum\:area=6cm×10cm=60cm²}$

$\small\mathbf{Again\: applying\:the\: formula:-}$

$\small\implies\mathbf{P=\frac{8000\:Pa×24cm²}{60cm²}}$

$\small\therefore\mathbf{P=2400\:Pa}$

$\small\boxed{\mathbf\red{∴The \:minimum\: pressure\:exerted\:by\:the}}$

$\small\boxed{\mathbf\red{cuboid\:is\:2400\:Pa}}$