Question

María regala a su padre un best seller por su cumpleaños. Elige la encuadernación de tapas duras que tiene forma de prisma rectangular, siendo sus medidas 18 cm de largo, 12 cm de ancho y 6 cm de grosor. Si sabemos que al envolverlo un 10% del envoltorio queda oculto por sí mismo, ¿cuál es la cantidad de papel de regalo empleada?

Answer 1

Answer:

María used only 792 square centimeters to cover the best seller.

Step-by-step explanation:

The volume of the best seller is about a rectangular prism, which is

$V= w \times l \times h$

Where $w$ is width, $l$ is length and $h$ is height.

In this case, we have

$w=12 \ cm\\l= 18 \ cm\\h= 6 \ cm$

Replacing values in the formula, we have

$V=12cm \times 18cm \times 6cm=1,296cm^{3}$

Now, according to the problem, 10% of paper covers the book, that means we need to find the suface area and then find the 90% of the paper missing. The formula for surface area is

$S=2wl+2lh+2hw$

Replacing values, we have

$S=2(12)(18)+2(18)(6)+2(6)(12)=432+216+144=792cm^{2}$

If 792 square centimeters is 10% of the total paper, then

$x=100\%\frac{792cm^{2} }{10\%} =7,920cm^{2}$

Therefore, there is 7,920 square centimeters of papers, but María used only 792 square centimeters to cover the best seller.