Question

a carpenter is fitting some bookcases to an alcove, using as much of the space as possible from floor to ceiling, a height of 2.5 m. The books to be fitted into the shelves are 210 mm high and a gap of at least 30 mm is necessary above each book so that they can be removed. The shelves are 20 mm thick. The alcove is 1.2 m wide. The bottom shelf should not be less than 300 mm from the ground, as the house-owner cannot bend down easily. How many shelves can be fitted into the alcove?

Answer 1

The number of shelves that fit in the alcove is given by the height of each shelve and the height of the bookshelf above the ground

The number of bookshelves that fit into alcove, is 8 bookshelves

Reason:

Height of the alcove = 2.5 m

Height of the books = 210 mm = 0.21 m

The gap above each book = 30 mm = 0.03 m

The thickness of the shelves = 20 mm = 0.02 m

Width of the alcove = 1.2 m

Height of the bottom shelf above the ground = 300 mm = 0.3 m

Required:

The number of shelves that can be fitted into the alcove

Solution;

Let x, represent the number of shelves that can be fitted into the alcove

We have;

An initial height of the bookshelves above the ground = 0.3 m

Height of a shelve, H = Height of books + Gap above books + Thickness of shelves

Height above ground, including the bottom shelve = 0.3 m

• $x = \dfrac{2.5 - (0.3)}{0.02 + 0.03 } = 8\frac{6}{13}\approx 8.46$

Therefore, the maximum number of whole bookshelves that can be fitted into alcove, x ≈ 8 bookshelves

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