Question

Тюлень массой 250 кг лежит на льдине. Толщина всей льдины равна 110 см, а высота надводной части - 10 см. Найдите площадь льдины в квадратных метрах. Плотность воды 1000 кг/м3 Плотность льда 900 кг/м3 Можно считать, что верхняя и нижняя поверхность льдины горизонтальны, боковые поверхности вертикальны.

Answer 1

Дано: Мтюл = 250кг
Нльд = 110см
Ннад = 10см
ро воды = 1000кг/м³
ро льда = 900кг/м³
g = 10 Н/кг
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S льд - ?
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Масса льдины Мльд = ро льд · H льд · S льд
Сила тяжести льдины и тюленя: Р = (ро льд · H льд · S льд + Mтюл) · g
Архимедова сила Fарх = ро воды · g · Sльд · (Н льд - Н над)
И она уравновешивает силу тяжести льдины и тюленя: Р = Fарх
(ро льд · H льд · S льд + Mтюл) · g = ро воды · g · Sльд · (Н льд - Н над)
или
ро льд · H льд · S льд + Mтюл = ро воды · Sльд · (Н льд - Н над)
900 · 1,1 · S льд + 250 = 1000 · Sльд · 1
 990 · Sльд + 250 = 1000 Sльд
10 Sльд = 250
Sльд = 25 (м²)
Ответ: 25м²

Answer 2

Calculation of the Iceberg's Surface Area

To find the surface area of the iceberg, we need to calculate the area of the top and bottom surfaces, as well as the area of the four vertical sides.

1. Area of the top and bottom surfaces: - The thickness of the entire iceberg is given as 110 cm, which is equivalent to 1.1 meters. - The height of the above-water part of the iceberg is given as 10 cm, which is equivalent to 0.1 meters. - The area of each of the top and bottom surfaces can be calculated as the product of the length and width of the iceberg. - Since the top and bottom surfaces are rectangular and have the same dimensions, we only need to calculate the area of one surface.

2. Area of the vertical sides: - The vertical sides of the iceberg are assumed to be rectangular. - The length of each vertical side can be calculated as the perimeter of the top surface of the iceberg. - The width of each vertical side is the height of the above-water part of the iceberg.

3. Calculation of the surface area: - The surface area of the iceberg is the sum of the areas of the top and bottom surfaces, as well as the areas of the four vertical sides.

Let's perform the calculations step by step.

1. Calculation of the area of the top and bottom surfaces: - The length and width of the iceberg can be calculated using the given thickness and the height of the above-water part. - Length of the iceberg = Length of the above-water part + 2 * Thickness - Width of the iceberg = Width of the above-water part + 2 * Thickness

Substituting the given values: - Length of the iceberg = 0.1 m + 2 * 1.1 m = 2.3 m - Width of the iceberg = 0.1 m + 2 * 1.1 m = 2.3 m

The area of each of the top and bottom surfaces is: - Area of the top and bottom surfaces = Length of the iceberg * Width of the iceberg

Substituting the calculated values: - Area of the top and bottom surfaces = 2.3 m * 2.3 m = 5.29 square meters

2. Calculation of the area of the vertical sides: - The length of each vertical side is the perimeter of the top surface of the iceberg. - Perimeter of the top surface = 2 * (Length of the iceberg + Width of the iceberg)

Substituting the calculated values: - Perimeter of the top surface = 2 * (2.3 m + 2.3 m) = 9.2 m

The area of each vertical side is: - Area of each vertical side = Perimeter of the top surface * Width of the above-water part

Substituting the given value: - Area of each vertical side = 9.2 m * 0.1 m = 0.92 square meters

3. Calculation of the surface area: - The surface area of the iceberg is the sum of the areas of the top and bottom surfaces, as well as the areas of the four vertical sides. - Surface area of the iceberg = 2 * (Area of the top and bottom surfaces) + 4 * (Area of each vertical side)

Substituting the calculated values: - Surface area of the iceberg = 2 * 5.29 square meters + 4 * 0.92 square meters - Surface area of the iceberg = 10.58 square meters + 3.68 square meters - Surface area of the iceberg = 14.26 square meters

Therefore, the surface area of the iceberg is approximately 14.26 square meters.