Question

# A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is $30cm$ long, $25cm$ wide and $25cm$ high. What is the area of the glass? How much of tape is needed for all the $12$ edges?

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Solution

## Step-1: Calculate the total surface area of the greenhouse according to its shape:The shape of the herbarium is a cuboid. Hence, the total surface area is the sum of six rectangular facesThe total surface area of a cuboid is given asTotal surface area$=2\left(lb+bh+lh\right)$where, $l$ is the length, $b$ is the breadth and $h$is the height of the cuboid.Substituting the values we get$⇒$Total surface area $=2\left(30×25+25×25+30×25\right)$$⇒$ $=2\left(750+625+750\right)c{m}^{2}$$⇒$ $=2×2125c{m}^{2}$$⇒$Total surface area$=4250c{m}^{2}$Hence, the area of the glass required for the herbarium is $4250c{m}^{2}$Step-2: Calculate the length of tape needed for the edges:Since the herbarium is made entirely of glass planes and held together by tape, the length of tape needed for $12$ edges will be equal to the length of the $12$ edges$⇒$Length of edges$=4\left(l+b+h\right)$$⇒$ $=4\left(30+25+25\right)$ $⇒$ $=4×80$$⇒$Length of edges$=320cm$Hence, the length of tape needed for $12$ edges is $320cm$.

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