Question

The dimensions of a tin box are 12cm \[ \times \] 10.5 cm $ \times $8cm. If 20 such boxes are to be made, find the area of tin sheet required in ${m^3}$.

Answer 1

Hint: In this question use the direct formula to find the total surface area of a single cuboid which is \[T.S.A = 2\left[ {\left( {l \times b} \right) + \left( {b \times h} \right) + \left( {h \times l} \right)} \right]\]. After finding it for one cuboid, multiply it with 20 to get the answer.

Complete step-by-step answer:

The pictorial representation of the tin box is shown above.

As we see that the tin box has six surface whose dimensions are given as

$\left( {12cm \times 10.5cm \times 8cm} \right)$

So the length (l) of the tin box = 12 centimeter.

Breadth (b) of the tin box = 10.5 centimeter.

And height (h) of the tin box = 8 centimeter.

So the total surface area of the tin box is

\[ \Rightarrow T.S.A = 2\left[ {\left( {l \times b} \right) + \left( {b \times h} \right) + \left( {h \times l} \right)} \right]\] $cm^2$.

Now substitute the values in this equation we have,

\[ \Rightarrow T.S.A = 2\left[ {\left( {12 \times 10.5} \right) + \left( {10.5 \times 8} \right) + \left( {8 \times 12} \right)} \right]\] $cm^2$.

Now simplify the above equation we have,

$ \Rightarrow T.S.A = 2\left[ {126 + 84 + 96} \right] = 2\left( {306} \right) = 612{\text{ c}}{{\text{m}}^2}$

Now we have to make 20 such tin boxes so the area (A) of the sheet required is 20 multiplied by the total surface area of one tin box.

$ \Rightarrow A = 20 \times \left( {T.S.A} \right)$

$ \Rightarrow A = 20\left( {612} \right) = 12240{\text{ c}}{{\text{m}}^2}$

Now as we know that 100 cm = 1 m.

Now squaring on both sides we have,

Therefore 1 $m^2$ = 10000 $cm^2$.

So 1 $cm^2$ = (1/10000) $m^2$.

Therefore 12240 $cm^2$ = (12240/10000) $m^2$.

                                       = 1.224 $m^2$.

So the required area of tin sheet is 1.224 square meter.

So this is the required answer.

Note: There is always a confusion between T.S.A and C.S.A of a cuboid. The T.S.A of cuboid is equal to the sum of the areas of its six rectangular faces and the curved surface area is equal to the sum of the four surfaces of cuboid, the top and the bottom is excluded from the C.S.A.