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 greater lateral surface area and by how much?

Answer 1

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

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

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

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

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

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

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

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

$\sf{Lateral\: surface\: area\: of\: cubical\: box = 4 (side)^2}$

$\sf{= 4(10)^2}$

$\sf{= 400 cm^2}$

$\sf{Lateral \:surface\: area\: of\: cuboidal\: box = 2[lh+bh]}$

$\sf{= [2(12.5×8+10×8)]}$

$\sf{= (2×180) = 360}$

$\:$

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

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

$\sf{=400cm^2–360cm^2 = 40 cm^2}$

$\sf{Therefore\:, the\: lateral \:surface\: area\: of \:the}$ $\sf{cubical\:box\: is \:greater \:than\: that \:of \:the\: cuboidal\: box\: by}$ $\sf{40 cm^2}$