Surface area and Volume (Part - 4)
1. Om 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 15 cm * 20 cm * 5 cm and the smaller od dimensions 15
cm * 10 cm * 5 cm . For all the overlaps , 5 % of the total surface area
required extra . If the cost of the cardboard is 4 Rs for 1000 cm^2 , find the
cost of cardboard required for supplying 250 boxes of each kind .
Sol. For bigger box
Length of box l = 15 cm , breath b = 20 cm and height h = 5
cm
Total surface area of 1 bigger box = 2 ( l b + b h + h l )
Total surface area of 1 bigger box = 2 ( 15 * 20 + 20 * 5 +
5 * 15 )
Total surface area of 1 bigger box = 2 ( 300 + 100 + 75 )
Total surface area of 1 bigger box = 2 ( 475 )
Total surface area of 1 bigger box = 950 cm^2
Area of cardboard for overlap = 5 % of 950 cm^2 = 950 * ( 5
/ 100 ) = 47.5 cm^2
Total area of cardboard for 1 bigger box = 950 + 47.5 = 997.5
cm^2
Therefore , the area of cardboard for 250 bigger boxes = 250
* 997.5 cm^2 = 249375 cm^2
For smaller box
Length of box l = 15 cm , breath b = 10 cm and height h = 5
cm
Total surface area of 1 bigger box = 2 ( l b + b h + h l )
Total surface area of 1 bigger box = 2 ( 15 * 10 + 10 * 5 +
5 * 15 )
Total surface area of 1 bigger box = 2 ( 150 + 50 + 75 )
Total surface area of 1 bigger box = 2 ( 275 )
Total surface area of 1 bigger box = 550 cm^2
Area of cardboard for overlap = 5 % of 550 cm^2 = 550 * ( 5
/ 100 ) = 27.5 cm^2
Total area of cardboard for 1 bigger box = 550 + 27.5 = 577.5
cm^2
Therefore , the area of cardboard for 250 bigger boxes = 250
* 577.5 cm^2 = 144375 cm^2
S the area of cardboard for 500 boxes = 249375 + 144375 =
393750 cm^2
Total cost of cardboard at the rate of Rs 4 per 1000 cm^2 =
( 393750 * 4 ) / 1000 = Rs 1575
Hence , the total cost of cardboard for 500 boxes is Rs 1575
.
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| maths ncert solutions |
2. Om 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 20 cm * 20 cm * 5 cm and the smaller od dimensions 10
cm * 12 cm * 5 cm . For all the overlaps , 5 % of the total surface area
required extra . If the cost of the cardboard is 4 Rs for 1000 cm^2 , find the
cost of cardboard required for supplying 250 boxes of each kind .
Sol. For bigger box
Length of box l = 20 cm , breath b = 20 cm and height h = 5
cm
Total surface area of 1 bigger box = 2 ( l b + b h + h l )
Total surface area of 1 bigger box = 2 ( 20 * 20 + 20 * 5 +
5 * 20 )
Total surface area of 1 bigger box = 2 ( 400 + 100 + 100 )
Total surface area of 1 bigger box = 2 ( 600 )
Total surface area of 1 bigger box = 1200 cm^2
Area of cardboard for overlap = 5 % of 1200 cm^2 = 1200 * (
5 / 100 ) = 60 cm^2
Total area of cardboard for 1 bigger box = 1200 + 60 = 1260
cm^2
Therefore , the area of cardboard for 250 bigger boxes = 250
* 1260 cm^2 = 315000 cm^2
For smaller box
Length of box l = 10 cm , breath b = 12 cm and height h = 5
cm
Total surface area of 1 bigger box = 2 ( l b + b h + h l )
Total surface area of 1 bigger box = 2 ( 10 * 12 + 12 * 5 +
5 * 10 )
Total surface area of 1 bigger box = 2 ( 120 + 60 + 50 )
Total surface area of 1 bigger box = 2 ( 230 )
Total surface area of 1 bigger box = 460 cm^2
Area of cardboard for overlap = 5 % of 460 cm^2 = 460 * ( 5
/ 100 ) = 23 cm^2
Total area of cardboard for 1 bigger box = 460 + 23 = 483
cm^2
Therefore , the area of cardboard for 250 bigger boxes = 250
* 483 cm^2 = 120750 cm^2
S the area of cardboard for 500 boxes = 315000 + 120750 =
435750 cm^2
Total cost of cardboard at the rate of Rs 4 per 1000 cm^2 =
( 435750 * 4 ) / 1000 = Rs 1743
Hence , the total cost of cardboard for 500 boxes is Rs 1743
.
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