Question

A cubical box has each edge 5cm and another cuboidal box is 12.5 cm × 10 cm × 8 cm then which box has the greater lateral surfacearea and by how much?​

Answer 1

FINAL ANSWER:-

cuboid have larger lateral surface area by $310cm^{2}$

GIVEN:-

• cube (s) = $5\:cm$

• $dimensions \:of \:cuboid \:\:$ ⇒$l=12.5cm\\b=10cm\\h=8cm$

FORMULAS USED:-

• $CSA\:of\:cuboid=2(lb+bh)$

• $CSA\:of\:cube=4s^{2}$

TO FIND:-

which box has the greater lateral surface area and by how much

SOLUTION:-

$CSA\:of\:cuboid=2(lb+bh)$

$=2(12.5*10 + 1 0 *8 ) \\=2(125+80)\\=2(205)\\=410cm^{2}$

$CSA\:of\:cube=4s^{2}$

$=4(5)^{2}\\=4(25)\\=100cm^{2}$

$410>100\\CSA\:of\:cuboid>CSA\:of\:cube$

so

$=410-100\\=310cm^{2}$

hence cuboid have larger lateral surface area by $310cm^{2}$

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SOME IMPORTANT FORMULAS:-

$TSA\:of\:cylinder=2\pi rh +2\pi r^{2}\\TSA\:of\:hemisphere=3\pi r^{2}\\TSA\:of\:sphere=4\pi r^{2}\\TSA\:of\:cone=\pi r(r+l)\:\:or \:\:\pi rl + \pi r^{2}\\TSA\:of\:cube=6s^{2}\\TSA\:of\:cuboid=2(lb+lh+bh)\\\\CSA\:of\:cylinder=2\pi rh\\CSA\:of\:hemisphere=2\pi r^{2}\\CSA\:of\:sphere=4\pi r^{2} (same\:as\:TSA\:of\:sphere)\\CSA\:of\:cone=\pi rl\\CSA\:of\:cube=4s^{2}\\CSA\:of\:cuboid=2(lb+bh)$

Answer 2

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