Question

a plastic box 1.5m long, 1.25m wide and 65cm deep is to be made. it is to be open at the top. ignoring the thickness of the plastic sheet, determine i)the area of the sheet required for making the box. ii)the cost of sheet for it, if a sheet measuring 1msquare costs Rs.20

Answer 1

(i) The area of the sheet required is 5.45
`m^2.`

(ii) Cost of the sheet is Rs 109.

Solution:

Given length of the box (l) = 1.5 m

breadth of the box (b) = 1.25 m

depth of the box (h) = 65 cm =
`(65)/(100)` = 0.65 m

Top of the box is open.

(i) To find the area of the sheet required.

Area of the sheet required = Surface area of cuboid – Area of top

= 2(lb + bh + lh) – lb

= 2(1.5 × 1.25 + 1.25 × 0.65 + 1.5 × 0.65) – (1.5 × 1.25)

= 2(1.875 + 0.8125 + 0.975) – 1.875

= 2(3.6625) – 1.875

= 7.325 – 1.875

= 5.45 sq. m

Thus, area of the sheet required is 5.45
`m^2.`

(ii) To find the cost of the sheet.

Cost of sheet per 1
`m^2` = Rs 20

Cost of sheet of 5.45
`m^2` = Rs (5.45 × 20) = Rs 109

Hence (i) The area of the sheet required is 5.45
`m^2.`

(ii) Cost of the sheet is Rs 109.