Ex 13.1, 7
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 250 boxes of each kind.
For bigger box
Length of bigger box = 25 cm
Breadth of bigger box = 20 cm
Height of bigger box = 5 cm
Total surface area of bigger box = 2(lb + lh + bh)
= [2(25 × 20 + 25 × 5 + 20 × 5)] cm2
= [2(500 + 125 + 100)] cm2
= 1450 cm2
Extra area required = 5% × Surface Area of bigger box
= 5/100 × 1450
= 72.5 cm2
Total area required for 1 bigger box
= Total Surface Area + Extra area required
= (1450 + 72.5) cm2
= 1522.5 cm2
Total area required for 250 box
= Area of 1 box × 250
= (1522.5 × 250) cm2
= 380625 cm2
For smaller box
Length of smaller box = 15 cm
Breadth of smaller box = 12 cm
Height of smaller box = 5 cm
Total surface area of smaller box = 2(lb + lh + bh)
= [2(15 ×12 + 15 × 5 + 12 × 5] cm2
= [2(180 + 75 + 60)] cm2
= (2 × 315) cm2
= 630 cm2
Extra area required = 5% × Surface Area of smaller box
= 5/100 × 630
= 31.5 cm2
Total area required for 1 smaller box = Surface Area + Extra Area
= (630 + 31.5) cm2
= 661.5 cm2
Area of cardboard sheet required for 250 such smaller boxes
= Total area × 250
= (250 × 661.5) cm2
= 165375 cm2
Total cardboard sheet required
= Area of 250 big box + Area of 250 smaller box
= (380625 + 165375) cm2
= 546000 cm2
Cost of 1000 cm2 cardboard sheet = Rs 4
Cost of 1 cm2 cardboard sheet = Rs 1/1000 × 4
Cost of 546000 cm2 cardboard sheet = Rs ((546000 × 4)/1000)
= Rs 2184
Therefore, the cost of cardboard sheet required for 250 such boxes of each kind will be Rs 2184.

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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