Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm × 20 cm × 5 cm and the smaller of dimensions 15 cm × 12 cm × 5 cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs. 4 for 1000 cm2, find the cost of cardboard required for supplying 300 boxes of each kind.
Answers
Given:-
The bigger of dimensions 25 cm× 20 cm× 5 cm and the smaller dimensions 15 cm× 12 cm×5cm.
all the overlaps, 5% of total surface area is required extra.
the cost of cardboard is rs 4 for 1000 cm square.
To find:-
Find the cost of cardboard required for supplying 250 boxes of each kind.
Solutions:-
Length of bigger box = 25cm
Breadth of bigger box = 20cm
Height of bigger box = 5cm
Total surface area bigger box = 2(lb + bh + hl)
= 2(25 × 20 + 20 × 5 + 5 × 25)
= 2(500 + 100 + 125)
= 2 × 725
= 1450cm²
Extra area required for overlapping = 1450 × 5 / 100
= 1450/20
= 72.5cm²
While considering all overlaps total of 1 bigger box.
= 1450 + 72.5
= 1522.5cm²
Area of cardboard sheet required for 250 such bigger boxes.
= 1522.5 × 250
= 380625cm²
Total surface area of smaller box.
= 2(15 × 12 + 15 × 5 + 12 × 5)
= 2(180 + 75 + 60)
= 2 × 315
= 630
Therefore,
Extre area of required for overlapping.
= 630 × 5 / 100
= 63/2
= 31.5cm²
Total surface area of 1 smaller box while considering all overlaps.
= 630 + 31.5
= 661.5cm²
Area of cardboard sheet required for 250 smaller boxes.
= 250 × 661.5
= 165375cm²
Total cardboard sheet required = 380632 + 165375
= 546000cm²
Cost of 1000cm² cardboard sheet = Rs 4.
Cast of 546000cm² cardboard sheet.
= Rs (546000/1000 × 4)
= Rs 546 × 4
= Rs 2184
Hence, the cost of cardboard sheet required for 250 such boxes of each will be Rs 2184.
Total S.A of bigger box
- 2(lb+bh+lh)
- 2(25×20+25×5+20×5) cm²
- 2(500+125+100)
- 1450 cm²
For overlapping extra area required = (450×5)/100
- 72.5 cm²
Total S.A (including overlaps)
- 1450+72.5=1522.5 cm²
Area of cardboard sheet for 250 such boxes
- (1522.5×250) cm²
Total S.A of smaller box
- 2(15×12+15×5+12×5)cm²
- 630 cm²
For overlapping area required
- (630×5)/100
- 31.5 cm²
Total S.A (including overlaps)
- 630+31.5
- 661.5 cm²
Area of cardboard sheet required for 250 such boxes
- 250×661.5cm²
- 165375 cm²
Total cardboard sheet required =380625+165375
- 54000 cm²
Cost of 1000 cm² cardboard sheet
- Rs.4
Cost of 546000 cm² cardboard sheet
- Rs. (546000×4)/1000
- Rs. 2184