Question

a cubical box has each edge 10cm and another cuboidal box is 12.5cm long 10cm wide and 8cm high which box has the smaller total surface area and by how much ​

Answer 1

$\sf\large{\underline{\underline{\red{Solution:-}}}}$

$\sf{\orange{(i) \:Lateral \:surface\: area \:of \:cubical \:box}}$$\sf{= 4a^2 = 4 \times 102 = 400 cm^2}$

$\sf{Lateral \:surface \:area\: of \:cuboidal \:box = 2h\: (l + b)}$

$\sf{ = 2 \times 8\:(12.5 +10) = 16 \times 22.5 = 360 cm^2}$

$\sf{Thus, \:lateral \:surface\: area\: of \:cubical\: box\: is\: greater \:by:-}$

$\sf{(400 cm^2- 360 cm^2)}$

$\sf{\fbox{\color{red}{=40\:cm^2}}}$

$\sf{\orange{(ii)\: Total\: surface \:area\: of \:cubical\: box }}$

$\sf{= 6a^2 = 6 x 102 cm^2 = 600 cm^2}$

$\sf{Total \:surface \:area \:of\: cuboidal \:box = 2\: (lb + bh + hl)}$

$\sf{= 2\:(12.5 \times 10 + 10 \times 8 + 8 \times 12.5)}$

$\sf{= 2\:(125 + 80 + 100) = 2 x 305\:cm^2 = 610 \:cm^2}$

$\sf{Thus,\: total\: surface \:area\: of\: cuboidal\: box\: is\: greater }$$\sf{by \:(610 - 600) \:cm^2}$

$\sf{\fbox{\color{red}{= 10\: cm^2}}}$