Question

Cardboard boxes of two different sizes are made. The bigger has dimensions $$20\text{ cm}, 15\text{ cm}$$ and $$5\text{ cm}$$ and the smaller dimensions $$16\text{ cm}, 12\text{ cm}$$ and $$4\text{ cm}$$. $$5\%$$ of the total surface area is required extra for all overlaps. If the cost of the cardboard is $$\text{Rs. }20$$ for one square meter, find the cost of the cardboard for supplying $$200$$ boxes of each kind.

Answer 1

For bigger box:

Length of the bigger box $$20\text{ cm}$$

Breadth of the bigger box $$=15\text{ cm}$$

Height of thr bigger box $$=5\text{ cm}$$

So, Total Surface Area of bigger box $$=2(lb+bh+hl)$$

$$=2(20\times 15+15\times 5+5\times 20)$$

$$=2(300+75+100)$$

$$=2(475)$$

$$=950\text{ cm}^2$$

For Smaller box:

Length of the smaller box $$=16\text{ cm}$$

Breadth of the smaller box $$=12\text{ cm}$$

Height of the smaller box $$=4\text{ cm}$$

So, Total Surface Area of smaller box $$=2(lb+bh+hl)$$

$$=2(16\times 12+12\times 4+4\times 16)$$

$$=2(192+48+64)$$

$$=2(304)$$

$$=608\text{ cm}^2$$

Total surface area of $$200$$ boxes of each type $$=200(950+608)$$

$$=200\times 1558$$

$$=311600\text{ cm}^2$$

Extra Area Required $$=5\%$$ of $$200(950+608)$$

$$=\dfrac{5}{100}\times 1558 \times 200$$

$$=15580\text{ cm}^2$$

So, Total cardboard Required $$=311600+15580$$

$$=327180\text{ cm}^2$$

$$=\dfrac{327180}{10000}$$

$$=32.718 \text{ m}^2$$

Cost of Cardboard for $$1m^2=\text{Rs. }20$$

Cost of cardboard for $$32.718\text { m}^2=20\times 32.718$$

$$=\text{Rs. } 65.436$$

Hence, the cost of the cardboard for supplying $$200$$ boxes of each kind is $$\text{Rs. }65.436$$.