Question

A box 20 cm long, 10 ,cm wide and 0.7 cm is to be made which is open from the top. Find the a)area of cardboard required to make the box.b)cost of cardboard@rs 2per 5sqcm

Answer 1

Given data : A box 20 cm long, 10 cm wide and 0.7 cm height is to be made which is open from the top.

To find : a) area of cardboard required to make the box. b) cost of cardboard Rs 2 per 5 cm².

Solution : Here we know that, area of box is equal area of cardboard, so firstly we have to find out total surface area of the box.

Here,

• Length, L = 20 cm
• Width, W = 10 cm
• Height, H = 0.7 cm

By formula : total surface area of cuboid

⟹ Total surface area of cuboid = 2LW+2LH+2HW

Now,

⟹ TSA of the box = 2LW+2LH+2HW

⟹ TSA of the box = 2 * 20 * 10 + 2 * 20 * 0.7 + 2 * 0.7 * 10

⟹ TSA of the box = 2 * 200 + 2 * 14 + 2 * 7

⟹ TSA of the box = 400 + 28 + 14

⟹ TSA of the box = 428 + 14

⟹ TSA of the box = 442 cm²

Now, we need to find out area of upper surface of box,

⟹ Area upper surface = L * W

⟹ Area upper surface = 20 * 10

⟹ Area upper surface = 200 cm²

To find out, area of box which is open from the top,

⟹ Area of box = TSA of the box - Area upper surface

⟹ Area of box = 442 - 200

⟹ Area of box = 242 cm² ----{1}

Now, a/c to question

⟹ cost of cardboard = (Area of box/5) * 2

⟹ cost of cardboard = (242/5) * 2

⟹ cost of cardboard = 48.4 * 2

⟹ cost of cardboard = Rs 96.8

{Verification :

⟹ Area of box = (cost of cardboard * 5)/2

⟹ Area of box = (96.8 * 5)/2

⟹ Area of box = 484/2

⟹ Area of box = 242 cm²}

Answer : Area of cardboard required to make the box is 242 cm² and cost of cardboard is Rs 96.8.