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The-Object-shown-in-the-diagram-is-made-by-gluing-together-the-adjacent-faces-of-six-wooden-cubes-each-having-edges-of-length-2-cm-Find-the-total-surface-area-of-the-object-in-square-centimetres-




Question Number 16938 by Tinkutara last updated on 28/Jun/17
The Object shown in the diagram is  made by gluing together the adjacent  faces of six wooden cubes, each having  edges of length 2 cm. Find the total  surface area of the object in square  centimetres.
$$\mathrm{The}\:\mathrm{Object}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{the}\:\mathrm{diagram}\:\mathrm{is} \\ $$$$\mathrm{made}\:\mathrm{by}\:\mathrm{gluing}\:\mathrm{together}\:\mathrm{the}\:\mathrm{adjacent} \\ $$$$\mathrm{faces}\:\mathrm{of}\:\mathrm{six}\:\mathrm{wooden}\:\mathrm{cubes},\:\mathrm{each}\:\mathrm{having} \\ $$$$\mathrm{edges}\:\mathrm{of}\:\mathrm{length}\:\mathrm{2}\:\mathrm{cm}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{total} \\ $$$$\mathrm{surface}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{object}\:\mathrm{in}\:\mathrm{square} \\ $$$$\mathrm{centimetres}. \\ $$
Commented by Tinkutara last updated on 28/Jun/17
Commented by mrW1 last updated on 07/Jul/17
i see in this picture each time something  different. it changes when i look at it.  i see no cubes.
$$\mathrm{i}\:\mathrm{see}\:\mathrm{in}\:\mathrm{this}\:\mathrm{picture}\:\mathrm{each}\:\mathrm{time}\:\mathrm{something} \\ $$$$\mathrm{different}.\:\mathrm{it}\:\mathrm{changes}\:\mathrm{when}\:\mathrm{i}\:\mathrm{look}\:\mathrm{at}\:\mathrm{it}. \\ $$$$\mathrm{i}\:\mathrm{see}\:\mathrm{no}\:\mathrm{cubes}. \\ $$
Answered by ajfour last updated on 28/Jun/17
A=4cm^2   if not glued together  A_T =6×6×A  when glued as shown     surface area S= A_T −2×5A     S=26A=26×4cm^2 =104cm^2 .
$$\mathrm{A}=\mathrm{4cm}^{\mathrm{2}} \\ $$$$\mathrm{if}\:\mathrm{not}\:\mathrm{glued}\:\mathrm{together} \\ $$$$\mathrm{A}_{\mathrm{T}} =\mathrm{6}×\mathrm{6}×\mathrm{A} \\ $$$$\mathrm{when}\:\mathrm{glued}\:\mathrm{as}\:\mathrm{shown} \\ $$$$\:\:\:\mathrm{surface}\:\mathrm{area}\:\mathrm{S}=\:\mathrm{A}_{\mathrm{T}} −\mathrm{2}×\mathrm{5A} \\ $$$$\:\:\:\mathrm{S}=\mathrm{26A}=\mathrm{26}×\mathrm{4cm}^{\mathrm{2}} =\mathrm{104cm}^{\mathrm{2}} . \\ $$
Commented by Tinkutara last updated on 28/Jun/17
Thanks Sir!
$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$

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