Question

plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened 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 1m2 costs ₹20.​

Answer 1

Question :-

A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened 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 ${1m}^{2}$ costs ₹20.

Given :-

• Length of box = 1.5m

• Breadth of box = 1.25m

• Depth of box = 65cm

• box is opened at top

• Cost of sheet per ${m}^{2}$ = Rs.20

To find :-

• The area of the sheet required for making the box?

• The cost of sheet for it, if a sheet measuring ${1m}^{2}$ costs ₹20?

Solution :-

Here,

• length (l) = 1.5 m,

• breadth(b) = 1 .25 m

• height (h) = 65 cm = $\dfrac{65}{100}$ = 0.65 m

∴ It is open from the top.

∴ Its surface area

= [Lateral surface area] + [Base area]

= [2(1 + b)h] + [lb]

= [2(1.50 + 1.25)0.65] ${m}^{2}$ + [1.50 x 1.25] ${m}^{2}$

= [2 x 2.75 x 0.65] ${m}^{2}$ + [1.875] ${m}^{2}$

= 3.575 ${m}^{2}$ + 1.875 ${m}^{2}$

= 5.45 ${m}^{2}$

__________

∴ Area of the sheet required for making the box

= 5.45 ${m}^{2}$

____________

(ii) Cost of 1 ${m}^{2}$ sheet = Rs. 20

Cost of 5.45 ${m}^{2}$ sheet = Rs. (20 x 5.45)

= Rs. 109

Hence, cost of the required sheet = Rs. 109

Answer 2

$\huge\underline{\bf \orange{Answer :}}$

Here,

length (l) = 1.5 m,

breadth(b) = 1 .25 m

height (h) = 65 cm = 100/65

= 0.65 m

∴ It is open from the top.

∴ Its surface area

= [Lateral surface area] + [Base area]

= [2(1 + b)h] + [lb]

= [2(1.50 + 1.25)0.65] m² + [1.50 x 1.25] m²

= [2 x 2.75 x 0.65] m² + [1.875] m²

= 3.575 m² + 1.875 m²

= 5.45 m²

__________

∴ Area of the sheet required for making the box

= 5.45m²

____________

(ii) Cost of 1 m² sheet = Rs. 20

Cost of 5.45m² sheet = Rs. (20 x 5.45)

= Rs. 109

Hence, cost of the required sheet = Rs. 109