Question

Из 12 досок длиной 5,5 м и шириной 0,3 м сделали ящик без крышки .размеры ящика :длина -2,2 м,ширина-1,4м,высота-1,7м. Заходы досок при скреплении составили 4% всей поверхности ящика. Сколько процентов материала осталось неиспользованным ?

Answer 1

Периметр ящика составил (2,2 + 1,4 ) * 2 = 7,2 м
Площадь боковой поверхности равна : 7,2 * 1,7 = 12,24 м2
Площадь дна ящика : 2,2 * 1,4 = 3,08 м2
Общая площадь равна : 12,24 + 3,08 = 15,32 м2
Общая площадь с учетом захода досок равна  : 15,32 *(1+4/100) = 15,93 м2
Площадь одной доски = 5,5 * 0,3 = 1,65 м2
Досок израсходовано : 15,93 / 1,65 = 9,7 = 10,0 досок
Осталось не использовано  (12 - 10) /12 * 100 =  16,7 % материала  

Answer 2

Calculation of the Material Used

To calculate the amount of material used in making the box, we need to find the total surface area of the box and then subtract the percentage of material wasted during assembly.

The dimensions of the box are as follows: - Length: 2.2 m - Width: 1.4 m - Height: 1.7 m

To find the total surface area of the box, we need to calculate the area of each side and then sum them up.

The area of the bottom and top sides (which are the same) can be calculated as the product of the length and width: - Bottom/Top area: 2.2 m * 1.4 m = 3.08 m²

The area of the front and back sides (which are the same) can be calculated as the product of the length and height: - Front/Back area: 2.2 m * 1.7 m = 3.74 m²

The area of the left and right sides (which are the same) can be calculated as the product of the width and height: - Left/Right area: 1.4 m * 1.7 m = 2.38 m²

Now, we can calculate the total surface area of the box by summing up the areas of all sides: - Total surface area: 2 * (Bottom/Top area) + 2 * (Front/Back area) + 2 * (Left/Right area) - Total surface area: 2 * 3.08 m² + 2 * 3.74 m² + 2 * 2.38 m² = 19.84 m²

Calculation of the Material Wasted

According to the given information, the wastage during assembly is 4% of the total surface area of the box.

To calculate the amount of material wasted, we can multiply the total surface area by the wastage percentage: - Material wasted: 19.84 m² * 4% = 0.794 m²

Calculation of the Material Unused

To find the amount of material unused, we need to subtract the material wasted from the total material used.

The total material used is equal to the total surface area of the box: - Total material used: 19.84 m²

To calculate the material unused, we subtract the material wasted from the total material used: - Material unused: Total material used - Material wasted - Material unused: 19.84 m² - 0.794 m² = 19.046 m²

Calculation of the Percentage of Material Unused

To calculate the percentage of material unused, we divide the material unused by the total material used and multiply by 100: - Percentage of material unused: (Material unused / Total material used) * 100 - Percentage of material unused: (19.046 m² / 19.84 m²) * 100 ≈ 96.03%

Therefore, approximately 96.03% of the material remained unused.