Question

A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm 25 cm wide and 25 cm high. (1). what is the area of the glass ? (2). how much of tape is needed for all the 12edges?​

Answer 1

$\Large\frak{\underline{\underline{Question:}}}$

A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm 25 cm wide and 25 cm high. (1). what is the area of the glass ? (2). how much of tape is needed for all the 12edges?

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$\Large\frak{\underline{\underline{Given:}}}$

Dimensions of herbarium

:$\implies{\boxed{\sf{\green{l = 30 cm, b = 25 cm, h = 25 cm}}}}$

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$\Large\frak{\underline{\underline{Answer:}}}$

${\sf{Tape \: needed\: for \:12\: edges=\:320\: cm}}$

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${\sf{Area\: of \:the\: glass=\:Total\:surface}}$

➤${\underline{\sf{Area \:of\: herbarium}}}$

➛${\sf{2(lb + bh + lh)}}$

➛ ${\sf{22(30×25+25×25+25\times30)}}$

➛ ${\sf{22(750+625+750)}}$

➛ ${\sf{22×2125}}$

➛ ${\sf{24250\:cm^2}}$

➤${\underline{\sf{Herbarium\: in\: the \:shape\: of \:cuboid}}}$

${\sf{So\: Length\: of \:the\: required\: tape \:will}}$

${\sf{2equal\: to\: total \:length\: of\: edges\: of \:cuboid.}}$

Length of the tape= 4(l + b + h)

➛${\sf{24(30 + 25 + 25) = 4× 80}}$

➛${\sf{2320 cm}}$

${\sf{Tape \: needed\: for \:12\: edges=\:320\: cm}}$

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Answer 2

Answer:

$\large{\underline{\mathrm{\green{Total\:\:\:surface\:\:\:area\:\:\::-}}}}$

$\\ \sf \: 2 \: ( \: lb \: + bh \: + \: hl \: ) \\ \\ \\ \implies \sf \: 2 \: (30 \times 25 + 25 \times 25 + 25 \times 30) \\ \\ \\ \implies \sf \: 2(750 + 625 + 750) \\ \\ \\ \implies \sf \: 2 \times 2125 \\ \\ \\ \implies \sf \blue{ 4250 \: {cm}^{2} }$

$\large{\underline{\mathrm{\red{Tape\:\:needed\:\:for\:\:all\:\:12\:\:edges :-}}}}$

$\\ \sf \implies \: (4 + l) \: + \: (4 \times b) \: + (4 \times h) \\ \\ \\ \sf \implies \: (4 \times 30) + (4 \times 25) + (4 \times 25) \\ \\ \\ \implies \sf \: 120 + 100 + 100 \\ \\ \\ \implies \sf \green{320 \: {cm}^{2} }$