Question

A cubical box has each edge 10 cm and another cuboidal box is 12.5cm long, 10 cm wide and 8 cm high. Which box has the smaller total surface area and by how much?

Answer 1

$\large{\underline{\underline{\textsf{\maltese\:{\red{Given}}}}}}$

$\sf{Side\: of\: a\: cubical\: box = 10cm}$

$\sf{Length, \:(l) \:of \:cuboidal\: box = 12.5 cm}$

$\sf{Breadth, \:(b) \:of \:cuboidal \:box = 10cm}$

$\sf{Height, (h) \:of \:cuboidal \:box = 8 cm}$

$\large{\underline{\underline{\textsf{\maltese\:{\red{To\: Find}}}}}}$

$\sf{Which\: box\: has\: the\: smaller\: total\: surface}$ $\sf{area \:and \:by \:how\:much\:?}$

$\large{\underline{\underline{\textsf{\maltese\:{\red{Solution}}}}}}$

$\sf{The \:total\: surface\: area\: of \:the\: cubical\: box}$

$\sf{= 6(side)^2 }$

$\sf{= 6(10 \:cm)^2}$

$\sf{= 600\: cm^2}$

$\sf{Total \:surface\: area\: of \:cuboidal \:box}$

$\sf{= 2[lh+bh+lb]}$

$\sf{= [2(12.5×8+10×8+12.5×100)]}$

$\sf{= 610\:cm^2}$

$\underline{\underline{\textsf{Difference:}}}$

$\sf{Total \:surface \:area \:of \:cuboidal \:box – Total \:surface\: area\: of \:cubical \:box}$

$\sf{=610\:cm^2–600cm^2 }$

$\sf{= 10\: cm^2}$

$\sf{Therefore,\: the\: total\: surface\: area \:of\: the}$ $\sf{cubical\:box\: is\: smaller \:than\: that \:of\: the}$ $\sf{cuboidal\:box\:by \:10cm^2}$

Answer 2

area of cubical box

≈6l²

=600 cm²

area of cuboidal box

=2(hw+hl+lw)

=2(80cm²+100cm²+125cm²)

=2(305cm²)

=610cm² ans...

610-600=10cm²