Question

There are 18 boxes on a shelf.

(a) How many boxes in total can be kept on the shelf without leaving any space?

(b) If the length and height of the shelf are doubled, how many boxes can be kept on the shelf now without leaving any space?

(c) If the length is halved and height of the shelf is doubled, how many boxes can be kept on the shelf now without leaving any space?

(d) If the length is doubled and height of the shelf is halved, how many boxes can be kept on the shelf now without leaving any space?

[4 MARKS]

Answer 1

Each part: 1 Mark

From visual estimation, each column contains 4 boxes.



(a) 6 columns can be fit in the shelf.

In the 5th column, there is space for 2 more boxes.

and in the 6th column, there is space for 4 boxes.

$\therefore$ Number of boxes on the full shelf = 18 + 2 + 4 = 24 boxes


(b) If the length of the shelf is doubled, the shelf can have 12 columns.

If the height of the shelf is doubled, then each column can have 8 boxes.

$\therefore$ Total number of boxes on the full new shelf:

= $12\times 8$

= 96 boxes


(c) If the length of the shelf is halved, the shelf can have 3 columns.

If the height of the shelf is doubled, then each column can have 8 boxes

$\therefore$ Total number of boxes on the full new shelf:

= $3\times 8$

= 24 boxes

(d) If the length of the shelf is doubled, the shelf can have 12 columns.

If the height of the shelf is doubled, then each column can have 4 boxes.

$\therefore$ Total number of boxes on the full new shelf:

= $12\times 4$

= 48 boxes