Question

Площадь основания цилиндра равен 2 см высота 12 Найдите площадь поверхности цилиндра​

Answer 1

Площадь основания цилиндра може бути знайдена шляхом використання формули для площі кола:

S = πr²

Оскільки радіус циліндра рівний половині діаметру, а діаметр циліндра є довжиною основи циліндра, то радіус дорівнює 1 см.

Тоді S = π(1²) = π кв.см

Щоб знайти площу поверхні циліндра, потрібно додати площу основи та площу згортки циліндра, що може бути знайдено за допомогою формули для площі прямокутної трапеції:

S = 2πrh + 2πr²

Оскільки висота циліндра дорівнює 12 см, а радіус - 1 см, то:

S = 2π(1)(12) + 2π(1²) = 24π + π = 25π кв.см.

Тому, площа поверхні циліндра дорівнює 25π кв.см.

Answer 2

Calculation of the Surface Area of a Cylinder

To find the surface area of a cylinder, we need to know the radius of the base and the height of the cylinder. In this case, the radius of the base is not given, but we are given the area of the base, which is 2 cm², and the height of the cylinder is 12 cm.

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

Area of the Bases

The area of the base of a cylinder is given by the formula A = πr², where A is the area and r is the radius of the base.

Since the area of the base is given as 2 cm², we can solve for the radius using the formula:

2 = πr²

Solving for r, we get:

r = √(2/π)

Using this value of r, we can calculate the area of the base.

Lateral Surface Area

The lateral surface area of a cylinder is given by the formula A = 2πrh, where A is the area, r is the radius of the base, and h is the height of the cylinder.

Using the calculated value of r and the given height of 12 cm, we can calculate the lateral surface area.

Total Surface Area

To find the total surface area of the cylinder, we add the areas of the two bases and the lateral surface area.

Let's calculate the surface area of the cylinder using the given information.

Calculation Steps:

1. Calculate the radius of the base using the formula r = √(2/π). 2. Calculate the area of the base using the formula A = πr². 3. Calculate the lateral surface area using the formula A = 2πrh. 4. Calculate the total surface area by adding the areas of the two bases and the lateral surface area.

Solution:

1. Calculate the radius of the base: - r = √(2/π) ≈ 0.7979 cm.

2. Calculate the area of the base: - A = πr² ≈ π(0.7979)² ≈ 2 cm².

3. Calculate the lateral surface area: - A = 2πrh = 2π(0.7979)(12) ≈ 60.384 cm².

4. Calculate the total surface area: - Total Surface Area = 2(Area of Base) + Lateral Surface Area - Total Surface Area = 2(2) + 60.384 ≈ 64.384 cm².

Therefore, the surface area of the given cylinder is approximately 64.384 cm².

Please let me know if you need any further assistance!