Question

A box is to be made by cutting off small squares from the corners of a square of thick paper and turning up the tabs.

The height of the box should be 5 centimetres and it should have a capacity of litre. What should be the length of a side of the square cut off? And the length of a side of the original square?

Answer 1

The box is made from a square paper by cutting off small squares from each of the corners

∴ Length of the box = Breadth of the box = a cm

Height of the box = 5 cm

Height of the box = Length of sides of the small squares which are cut off from the paper

⇒ Length of sides of the small squares = 5 cm

Capacity of the box =

We know that 1 L = 1000 cm³

∴ Volume of the box =

⇒ Length × Breadth × Height = 500 cm³

⇒ a × a × 5 = 500 cm³

⇒ (a)² = 100

⇒ a =

As length cannot be negative, a = 10.

∴ Length and breadth of the box = 10 cm

∴ Length of the side of the original square = (10 + 5 + 5) cm = 20 cm