The diagram shows a cuboid.
The width of the cuboid is 25 cm.
The end face of the cuboid is a square.
The volume of the cuboid is 1.25 m'.
a Work out the length of the cuboid.
b Work out the surface area of the cuboid.
Answers
Length (1) = 25 cm, Breadth (b) = 20 cm, Height (h) = 5 cm
∵ The box is like a cuboid and total surface area of a cuboid = 2(lb + bh + hl)
Area of a box = 2([25 × 20) + (20 × 5) + (5 × 25)] cm2 = 2[500 + 100 + 125] cm2 = 2[725] cm2 = 1450 cm2
Total surface area of 250 boxes = 250 × 1450 cm2 = 362500 cm2
For smaller box: l = 15 cm, b = 12 cm, h = 5 cm
Total surface area of a box = 2[lb + bh + hl]
= 2[(15 × 12) + (12 × 5) + (5 × 15)] cm2
= 2[180 + 60 + 75] cm2
= 2[315] cm2 = 630 cm2
⇒ Total surface area of 250 boxes = 250 × 630 cm2
= 157500 cm2
Now, total surface area of both kinds of boxes
= 362500 cm2 + 157500 cm2
= 5,20,000 cm2
Area for overlaps = 5% of [ total surface area]
∴ Total area of the cardboard required = [Total area of 250 boxes] + [5% of total surface area]
= 520000 cm2 + 26000 cm2
= 546000 cm2
Cost of cardboard:
∵ Cost of 1000 cm2 = Rs. 4