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.

1. What is the area of the glass?
2. How much of tape is needed for all the $12$ edges?

Answer 1

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 faces

The total surface area of a cuboid is given as

Total 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

$\Rightarrow$Total surface area $=2\left(30\times 25+25\times 25+30\times 25\right)$

$\Rightarrow$ $=2\left(750+625+750\right)c{m}^2$

$\Rightarrow$ $=2\times 2125c{m}^2$

$\Rightarrow$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

$\Rightarrow$Length of edges$=4\left(l+b+h\right)$

$\Rightarrow$ $=4\left(30+25+25\right)$

$\Rightarrow$ $=4\times 80$

$\Rightarrow$Length of edges$=320cm$

Hence, the length of tape needed for $12$ edges is $320cm$.