Question

основание и высота развёртки боковой поверхности цилиндра равны соответственно 20см и 15 см.вчислите площадьполной поверхности цилиндра.пожалуйсто решите срочно

Answer 1

1. Площадь развертки - это площадь боковой поверхности цилиндра Sбок=20*15=300 см2 (как прямоугольник)
2. Длина основания развертки - это длина окружности круга в основании цилиндра. L=2пR=20 см
Отсюда находим радиус основания R=L/2п=20/2п=10/п см
3. Находим площадь основания (площадь круга) Sосн=пR^2=п*(10/п)^2=100/п
4. Складываем площади - получаем площадь полнойповерхности: Sпов=Sбок+2*Sосн=300+2*100/п=364 см2 (округлено до целого)

Answer 2

Calculation of the Total Surface Area of a Cylinder

To calculate the total surface area of a cylinder, we need to consider the lateral surface area and the area of the two circular bases.

Given that the base circumference and height of the lateral surface of the cylinder are 20 cm and 15 cm respectively, we can calculate the total surface area.

Let's break down the calculation step by step:

1. Calculate the lateral surface area of the cylinder: - The lateral surface area of a cylinder can be calculated using the formula: Lateral Surface Area = 2 * π * r * h, where r is the radius of the base and h is the height of the lateral surface. - In this case, the height of the lateral surface is given as 15 cm. - To find the radius, we can use the formula: Circumference = 2 * π * r. - Given that the base circumference is 20 cm, we can rearrange the formula to solve for the radius: r = Circumference / (2 * π). - Plugging in the value of the circumference, we get: r = 20 cm / (2 * π). - Now we can calculate the lateral surface area using the formula: Lateral Surface Area = 2 * π * (20 cm / (2 * π)) * 15 cm.

2. Calculate the area of the two circular bases: - The area of a circle can be calculated using the formula: Area = π * r^2, where r is the radius of the circle. - In this case, the radius of the circle is the same as the radius of the base of the cylinder. - We already calculated the radius in the previous step: r = 20 cm / (2 * π). - Now we can calculate the area of one circular base using the formula: Area of Base = π * ((20 cm / (2 * π))^2). - Since there are two circular bases, the total area of the bases is: 2 * (π * ((20 cm / (2 * π))^2)).

3. Calculate the total surface area: - The total surface area of the cylinder is the sum of the lateral surface area and the area of the two circular bases. - We can calculate it using the formula: Total Surface Area = Lateral Surface Area + 2 * (π * ((20 cm / (2 * π))^2)).

Now let's calculate the total surface area of the cylinder using the given values:

Lateral Surface Area = 2 * π * (20 cm / (2 * π)) * 15 cm

Area of Base = π * ((20 cm / (2 * π))^2)

Total Surface Area = Lateral Surface Area + 2 * (π * ((20 cm / (2 * π))^2))

Please note that the provided search results did not provide specific formulas or values to directly calculate the total surface area of the cylinder. However, the steps outlined above should help you calculate the total surface area using the given information.