Question

A hollow metallic box without lid with outer dimension 20 cm by 18cm by 15cm and 2cm thick from all around is melt and cast into small cube of edge 2.5cm.how many such complete cubes can be made and what volume of metal would be left behind.​

Answer 1

$\underline { \pink { Outer \: dimensions \:of \:box:}}$

Length (L) = 20 cm,

Breadth (B) = 18 cm ,

Height (H) = 15 cm ,

$Thickness \: of \: the \:box (w) = 2\:cm$

$\underline { \pink { Inner\: dimensions \:of \:box:}}$

length (l) = L - 2w

= 20 - 2×2

= 20 - 4

= 16 cm ,

breadth (b) = B - 2w

= 18 - 4

= 14 cm ,

Height (h) = H - w

= 15 - 2

= 13 cm ,

$Volume \: of \: the \: hollow \:box\\ = LBH - lbh\\</p><p>= 20 \times 18 \times 15 - 16 \times 14 \times 13\\= 5400 - 2912\\=2488\: cm^{3}$

/* If the box melted and cast into small cubes */

$Edge \:of \: each \: cube = 2.5 \:cm$

$Volume \: of \: each \:cube = a^{3} \\= (2.5)^{3}\\= 15.625 \:cm^{3}$

$Let \: number \: small \: boxes \:made =n$

$n = \frac{ Volume \: of \:hollow \:box }{volume \:of \:each \:cube } \\= \frac{2488}{15.625} \\= 159.625$

/* Number of boxes should not be decimals */

$n = 159$

$Volume \: of \: remaining \: metal \\= Volume \: of \: box - 159 \times (volume \:of \:each \:box) \\= 2488 - 159 \times 15.625\\= 2488 - 2484.375\\= 3.625 \:cm^{3}$

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