Question

An aluminium trunk with outer dimensions 30 inch*18 inch*22 inch is made out a 1 - inch - thick sheet of aluminum. Find the inner volume of the trunk and also the volume of aluminium used in the box

Answer 1

$\underline { \blue { Outer \: dimensions \:of \: Aluminium \:trunk :}}$

$Length (L) = 30\: inches ,\\Breadth (B) = 18 \: inches \\Height(H) = 22 \: inches$

$Thickness \:of \:the \:sheet (w) = 1 \:inch$

$\underline { \blue { Inner\: dimensions \:of \: Aluminium \:trunk :}}$

$Length (l) = L - 2w \\= (30-2\times 1)\\= 28\: inches ,\\Breadth (b) =B - 2w \\= (18-2\times 1)\\= 16\: inches \\Height(h) = H - 2w \\= (22-2\times 1)\\= 20\: inches$

$\red{ Inner \: volume \:of \:the \:trunk } \\= l \times b \times h \\= 28 \times 16 \times 20 \\= 8960 \: cubic \:inches \: ---(1)$

$\red { Volume \:of \: aluminium \: used }$

$\red {in \:the \:box }\\= Volume \: of \:outer \:box - (1) \\= LBH - lbh \\= 30 \times 18 \times 22 - 8960\\= 11880 - 8960 \\= 2920 \: cubic \:inches \:--(2)$

Therefore.,

$\red{ Inner \: volume \:of \:the \:trunk }\\ \green {= 8960 \: cubic \:inches }$

$\red { Volume \:of \: aluminium \: used }$

$\red {in \:the \:box }\green {= 2920 \: cubic \:inches }$

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