Question

The dimensions of an oil tin are $26cm \times 26cm \times 45cm.$Find the area of the tin sheet required for making 20 such tins. If 1 square m of the tin sheet cost R.s. 10, find the cost of tin used for these 20 tins.

Answer 1

Hint- Here we will proceed by calculating area of oil tin by using the formula of total surface area of cuboid. Then we will find the cost of 20 oil tins using the calculated area of the tins.

Complete step-by-step answer:
As we are given with the dimensions of the oil tin-

Length of an oil tin = 26cm
Breadth of an oil tin = 26cm
Height of an oil tin = 45cm
Firstly, we will find the area of tin required for the sheet using the formula of total surface area of cuboid.
Total surface area of cuboid $ = 2\left( {length \times breadth + breadth \times height + length \times height} \right)$
Area of an oil tin required for sheet $ = 2\left[ {26 \times 26 + 26 \times 45 + 26 \times 45} \right]c{m^2}$
So the area of tin sheet required for making 20 sheets $ = 40\left[ {26 \times 26 + 26 \times 45 + 26 \times 45} \right]c{m^2}$
$ = 120640c{m^2}$
Converting $c{m^2}$ into ${m^2}$.
$ = \dfrac{{120640}}{{100 \times 100}}{m^2}$
Now we will find the cost of tin used for making 20 such tins when 1 square meter of the tin sheet cost R.s. 10 $ = \dfrac{{120640}}{{100 \times 100}} \times 10$
$ = \dfrac{{12064}}{{100}}$
= R.s. 120.64
Therefore, the area of the tin sheet required for making 20 oil tins is $120640c{m^2}$ and the cost of tin used for 20 oil tins is R.s. 120.64.
Note- We have to convert the area of tin calculated in centimeters to meters because in the question, the given dimension of tin sheet is in meters. We must be careful with this condition as many of us can get confused in this step.