A book is 10 cm x 18 cm long and 2 cm thick. It has a protective paper ‘jacket’ over the entire cover and folding 5 cm under the front and back covers. How much paper is needed for the ‘jacket’?
so the paper needs to be 10+2+10 to cover the front, spine, and back.
Add 5+5 for the overlap
This assumes the book is 18cm high, not 10cm high.
To find out how much paper is needed for the 'jacket' of the book, we need to calculate the surface area of the jacket.
First, let's calculate the surface area of the front cover, back cover, and spine.
The front and back covers have the same dimensions, so we'll calculate the surface area of one cover and then double it.
The surface area of a rectangle can be calculated by multiplying its length by its width.
The front and back covers have dimensions of 10 cm by 18 cm. So the surface area of one cover is 10 cm x 18 cm = 180 cm².
Since we need to fold 5 cm under the front and back covers, the width of the spine will be 2 cm + 5 cm + 5 cm = 12 cm.
The length of the spine will be the same as the height of the book, which is 18 cm.
So the surface area of the spine is 12 cm x 18 cm = 216 cm².
Now, let's calculate the surface area of the whole 'jacket'.
Since we have two covers and one spine, we need to add the surface area of the covers to the surface area of the spine.
The surface area of the covers is 2 x 180 cm² = 360 cm².
The total surface area of the 'jacket' is the sum of the surface area of the covers and the surface area of the spine, which is 360 cm² + 216 cm² = 576 cm².
Therefore, 576 cm² of paper is needed for the 'jacket' of the book.