Question

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

Answer 1

Hint:We will have to calculate the surface area of the greenhouse, which means that we need to calculate the total area of the greenhouse.
The formula that we are going to use to calculate the surface area of the greenhouse is:-
\[2\text{ }\left( l\times b\text{ }+\text{ }b\times h\text{ }+\text{ }l\times h \right)\]
Here, ‘l’ refers to the length, ‘b’ refers to the breadth and ‘h’ refers to the height of the greenhouse.
Secondly, we need to calculate the length of the tape that is needed to hold all the glass panes together, i.e. the length of tape required for all the 12 edges.
The formula that we are going to use to calculate the length of the tape required is:-
4 (l + b + h)
Here, ‘l’ refers to the length, ‘b’ refers to the breadth and ‘h’ refers to the height of the greenhouse.

Complete step-by-step answer:
Given: Dimensions of the greenhouse:-
Length = 30 cm, Breadth = 25 cm, Height = 25 cm
To find:
a) Surface area of the greenhouse.
Total surface area of the greenhouse = Area of the green house
                                                                                  = \[2\text{ }\left( l\times b\text{ }+\text{ }b\times h\text{ }+\text{ }l\times h \right)\]
                                                                                  = \[2\text{ }(30\times ~25+25~\times 25+~25~\times 30)\]
                                                                                  = 2 (750 + 625 + 750)
                                                                                 = \[2\times 2125\]
                                                                                 = $4250cm^2$
Therefore, the total area of the greenhouse, i.e. the surface area of the greenhouse is 4250 square centimeter.

b) Length of the tape required to hold the glass panes of the greenhouse.
Length of the required tape = Total length of edges of cuboid.
                                                                = 4 (l + b + h)
                                                                = 4 (30 + 25 + 25)
                                                                = \[4\times 80\]
                                                               = $320 cm$
So, the length of the tape required to hold the glass panes of the greenhouse is 320 centimeter.
Note:-One must do all the calculations in this question very carefully.Here,we have to calculate area of the glass including base.Suppose if base is not included then we to subtract area of base from the total surface area of glass i.e \[2\text{ }\left( l\times b\text{ }+\text{ }b\times h\text{ }+\text{ }l\times h \right)-l \times b\].And here,length of the tape means total length of cuboid which is given by 4 (l + b + h).Students should remember the important formula of surface area of cuboid and definitions of it for solving these types of problems.