Question

Ведро цилиндрической формы имеет высоту 4,9 дм, а диаметр дна 32см. Сколько квадратных дециметров листового железа необходимо для изготовления ведра, если на швы нужно добавить 5% всей поверхности ведра?

Answer 1

4,9:32;0,153125. 0,153125:5;0,30625

Answer 2

Calculation of the Surface Area of the Cylinder

To calculate the surface area of the cylindrical bucket, we need to find the area of the curved surface (lateral surface area) and the area of the base.

The formula for the lateral surface area of a cylinder is given by:

Lateral Surface Area = 2 * π * r * h

where π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cylinder.

The formula for the area of the base of a cylinder is given by:

Base Area = π * r^2

where r is the radius of the base.

In this case, the height of the cylinder is given as 4.9 dm and the diameter of the base is given as 32 cm. We need to convert these measurements to the same unit before proceeding with the calculations.

Converting the height to centimeters: 1 dm = 10 cm So, the height of the cylinder in centimeters is 4.9 dm * 10 cm/dm = 49 cm.

Converting the diameter to centimeters: The diameter is given as 32 cm.

Now, let's calculate the radius of the base using the formula:

Radius = Diameter / 2

Radius = 32 cm / 2 = 16 cm.

Calculation of the Surface Area of the Cylinder (continued)

Now that we have the height and radius in the same unit (centimeters), we can proceed with the calculations.

The lateral surface area of the cylinder is given by:

Lateral Surface Area = 2 * π * r * h

Substituting the values, we get:

Lateral Surface Area = 2 * 3.14159 * 16 cm * 49 cm

Calculating the lateral surface area, we find:

Lateral Surface Area = 6157.28 cm^2

The area of the base of the cylinder is given by:

Base Area = π * r^2

Substituting the values, we get:

Base Area = 3.14159 * (16 cm)^2

Calculating the base area, we find:

Base Area = 804.25 cm^2

Calculation of the Total Surface Area of the Cylinder

To calculate the total surface area of the cylinder, we need to add the lateral surface area and the base area.

Total Surface Area = Lateral Surface Area + Base Area

Substituting the values, we get:

Total Surface Area = 6157.28 cm^2 + 804.25 cm^2

Calculating the total surface area, we find:

Total Surface Area = 6961.53 cm^2

Calculation of the Additional Surface Area for Seams

The question states that an additional 5% of the total surface area of the bucket needs to be added for the seams.

To calculate the additional surface area, we multiply the total surface area by 5% (0.05).

Additional Surface Area = 0.05 * Total Surface Area

Substituting the value of the total surface area, we get:

Additional Surface Area = 0.05 * 6961.53 cm^2

Calculating the additional surface area, we find:

Additional Surface Area = 348.08 cm^2

Calculation of the Total Area of Sheet Metal Required

To calculate the total area of sheet metal required, we add the total surface area and the additional surface area.

Total Area of Sheet Metal Required = Total Surface Area + Additional Surface Area

Substituting the values, we get:

Total Area of Sheet Metal Required = 6961.53 cm^2 + 348.08 cm^2

Calculating the total area of sheet metal required, we find:

Total Area of Sheet Metal Required = 7309.61 cm^2

Therefore, 7309.61 square decimeters (dm^2) of sheet metal are required to manufacture the bucket, considering the additional surface area for the seams.

Please note that the calculations are based on the given dimensions and assumptions.