2) De una pieza de madera de 10yd 7,62cm se ha obtenido
trozos de 33cm cada una. ¿Qué longitud falta para completar
un trozo más, si en cada corte se pierde 1cm?
a) 5,02cm b) 2,6cm c) 28,98cm d) 29,98cm e) 310,2cm
To find the length that is missing to complete a piece after cutting it into 33cm pieces with a loss of 1cm in each cut, we can calculate as follows:
1. Total initial length of wood = 10yd 7.62cm
2. Convert everything to centimeters for consistency:
- 10 yards = 914.4 cm
- Total initial length = 914.4 cm + 7.62 cm = 922.02 cm
3. Length of each piece after cutting = 33 cm
4. Loss per cut = 1 cm
5. Number of pieces obtained = Total initial length / (Length of each piece + Loss per cut)
- Number of pieces = 922.02 cm / (33 cm + 1 cm) ≈ 27.88 pieces
6. As we can't have a fraction of a piece, we consider we have 27 complete pieces.
7. Length of wood used for 27 pieces = 27 pieces * (33 cm + 1 cm) = 27 * 34 cm = 918 cm
8. Length of wood left = Total initial length - Length used for 27 pieces
- Length left = 922.02 cm - 918 cm = 4.02 cm
Therefore, the length missing to complete one more piece is 4.02 cm. The closest answer choice is 5.02 cm (a).
