Question 5: A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.
(i) Which box has the greater lateral surface area and by how much?
Answer: Side of cube = 10 cm, for cuboid: l = 12.5 cm, b = 10 cm, h = 8 cm
Lateral surface area of cube `=4xx(si\de)^2=4xx10^2``=400 sq cm`
Lateral surface area of cuboid `=2h(l + b)=2xx8(12.5+10)``=16xx22.5=360 sq cm`
`(Di\ff\er\en\ce=400–360=40 sq m)`
Hence, lateral surface area of cube > lateral surface area of cuboid
(ii) Which box has the smaller total surface area and by how much?
Answer: Total surface area of cube `=6xxsi\de^2=6xx10^2=600 sq cm`
Total surface area of cuboid `=2(lb+bh+lh)``=2(12.5xx10+10xx8+12.5xx8)``=2(125+80+100)``=2xx305=610 sq cm`
`(Di\ff\er\en\ce=610–60=10 sq cm)`
Hence, total surface area of cube < total surface area of cuboid
Question 6: A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high.
(i) What is the area of the glass?
Answer: l = 30 cm, b = 25 cm, h = 25 cm
Total surface area `=2(lb + bh + lh`
`=2xx2125=4250 sq cm`
(ii) How much of tape is needed for all the 12 edges?
Answer: Number of each edge is 4
Hence, total length of edge `=4(l + b + h)``=4(25+30+25)``=4xx80=320 cm`
Question 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.
Answer: Dimensions of bigger box: l = 25 cm, b = 20 cm, h = 5 cm
Total surface area of bigger box `= 2(lb + bh + lh)`
`= 2(25xx20 + 20xx5 + 25xx5)`
`= 2(500 + 100 + 125)``= 2xx725 ``= 1450 sq cm`
5% of total surface area `= 1450xx5% = 72.5 sq cm`
Hence, area of required cardboard `= 1450 + 72.5 = 1522.75 sq cm`
Dimensions of smaller box: l = 15 cm, b = 12 cm, h = 5 cm
Total surface area of smaller box `= 2(lb + bh + lh)`
`= 2(15xx12 + 12xx5 + 15xx5)``= 2(180 + 60 + 75)``= 2xx315 = 630 sq cm`
5% of total surface area `= 630xx5% = 32.5 sq cm`
Area of required cardboard `= 630 + 32.5 = 662.5 sq cm`
Cost of cardboard for 250 boxes of bigger size `= 250xx1522.75xx4/100 ``= Rs. 1522.75`
Cost of cardboard for 250 boxes of smaller size `= 250xx662.50xx4/100`` = 662.50`
Total cost `= 1522.75 + 662.50 = Rs. 2185.25`
Question 8: Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4 m × 3 m?
Answer: l = 4m, b = 3 m, h = 2.5 m
Area of top `= lxxb = 4xx3 = 12 sq m`
Lateral surface area `= 2h(l + b)= 2xx2.5(4 + 3)``= 5xx7 = 35 sq m`
Total area `= 12 + 35 = 47 sq m`
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