Question

Gopal sweets placed an order of making 30 cm \[ \times \] 20 cm \[ \times \] 6 cm cardboard boxes for packing their sweets. For all overlaps, 4 % of the total area is required extra. If the cost of the cardboard is 25 paise for 100 \[c{m^2}\], find the cost of the cardboard used for making 1000 boxes.

Answer 1

Hint: Find the total surface area of one cardboard box using the formula \[S = 2(lb + bh + hl)\] and then multiply it with 1000 and add 4 % of the total area to itself to find the total area of cardboard used. Then multiply it with cost per sq. cm to find the total cost.

We need to find the total cost for making 1000 cardboard boxes of dimension 30 cm \[ \times \] 20 cm \[ \times \] 6 cm.

\[l = 30cm.........(1)\]

\[b = 20cm.........(2)\]

\[h = 6cm.........(3)\]

We know the total surface area of the cuboid of length l, breadth b, and height h is given as follows:

\[S = 2(lb + bh + hl)...........(4)\]

Substituting equations (1), (2), and (3) in formula (4), we get:

\[S = 2(30 \times 20 + 20 \times 6 + 6 \times 30)\]

Simplifying, we get:

\[S = 2(600 + 120 + 180)\]

\[S = 2(900)\]

\[S = 1800c{m^2}\]

We have 1000 cardboards, hence, we need to multiply the area by 1000.

\[S' = 1800c{m^2} \times 1000\]

\[S' = 1800000c{m^2}\]

It is given that 4 % of the total area is used for overlaps. Hence, the total area of cardboard used is an additional 4 % for overlaps.

Total area = S’ + 4 % of S’

Total area = \[1800000 + \dfrac{4}{{100}} \times 1800000\]

Total area = \[1800000 + 4 \times 18000\]

Total area = \[1872000c{m^2}\]

The cost of 100 sq. cm of cardboard is given to be 25 paise.

The cost of \[1872000c{m^2}\] area of the cardboard is then given as follows:

Total cost = \[\dfrac{{1872000}}{{100}} \times 25\]

Total cost = \[\dfrac{{1872000}}{4}\]

Total cost = \[468000paise\]

Converting it into rupees we have:

Total cost = \[Rs.4680\]

Hence, the total cost for buying 1000 boxes is Rs. 4680.

Note: Don’t forget that the order is for 1000 cardboards, so, you need to multiply the area of one cardboard with a thousand, otherwise, your answer will be wrong.