Questions: Дизайнер верстает макет обложки книги и рассчитывает ширину корешка по формуле h=a * n+2 * b, где a - толщина Одной страницы, n - число страниц в книге, b толщина переплетного картона. Вычислить толщину корешка, если в книге 288 стр. на бумаге толщиной 0,5 мм, причем в конце добавлена еще и иллюстрированная вклейка на 32 стр. на мелованной бумаге толщиной 1 мм, а толщина переплетного картона - 1,5 мм.

Solution Steps

To calculate the thickness of the book spine, we need to use the given formula \( h = a \cdot n + 2 \cdot b \). We will first calculate the total number of pages and their respective thicknesses, then apply the formula to find the spine thickness.

1. Calculate the total number of pages: sum the regular pages and the illustrated pages.
2. Calculate the total thickness contributed by the regular pages and the illustrated pages.
3. Add the thickness of the binding board (twice, as it is on both sides).
4. Sum these values to get the total spine thickness.

The thickness of one regular page is \( a_{\text{regular}} = 0.5 \) mm, and the number of regular pages is \( n_{\text{regular}} = 288 \).

The total thickness of the regular pages is: \[ \text{thickness}_{\text{regular}} = a_{\text{regular}} \cdot n_{\text{regular}} = 0.5 \, \text{mm} \times 288 = 144.0 \, \text{mm} \]

The thickness of one illustrated page is \( a_{\text{illustrated}} = 1 \) mm, and the number of illustrated pages is \( n_{\text{illustrated}} = 32 \).

The total thickness of the illustrated pages is: \[ \text{thickness}_{\text{illustrated}} = a_{\text{illustrated}} \cdot n_{\text{illustrated}} = 1 \, \text{mm} \times 32 = 32 \, \text{mm} \]

The thickness of the binding board is \( b = 1.5 \) mm. According to the formula \( h = a \cdot n + 2 \cdot b \), we need to add the thickness of the binding board twice (once for each side).

The total spine thickness is: \[ h = \text{thickness}_{\text{regular}} + \text{thickness}_{\text{illustrated}} + 2 \cdot b = 144.0 \, \text{mm} + 32 \, \text{mm} + 2 \times 1.5 \, \text{mm} = 179.0 \, \text{mm} \]

Final Answer