Question

Радиус основания цилиндра равен 6 м а расстояние от центра одного основания до точки окружности второго основания равно 10 м . найдите площадь боковой поверхности цилиндра

Answer 1

Площадь находится по формуле S=2ПrH
S=60П

Answer 2

Problem Analysis

We are given the radius of the base of a cylinder, which is 6 m, and the distance from the center of one base to a point on the circumference of the other base, which is 10 m. We need to find the lateral surface area of the cylinder.

Solution

To find the lateral surface area of a cylinder, we need to calculate the circumference of the base and multiply it by the height of the cylinder.

The circumference of the base can be found using the formula: C = 2πr, where r is the radius of the base.

The height of the cylinder can be found using the given information. The distance from the center of one base to a point on the circumference of the other base is equal to the height of the cylinder.

Let's calculate the lateral surface area step by step:

1. Calculate the circumference of the base: - The radius of the base is given as 6 m. - Using the formula C = 2πr, we can calculate the circumference as C = 2π(6) = 12π.

2. Calculate the height of the cylinder: - The distance from the center of one base to a point on the circumference of the other base is given as 10 m. - This distance is equal to the height of the cylinder.

3. Calculate the lateral surface area: - The lateral surface area of a cylinder is given by the formula A = Ch, where C is the circumference of the base and h is the height of the cylinder. - Substituting the values we calculated earlier, we have A = (12π)(10) = 120π.

Therefore, the lateral surface area of the cylinder is 120π square meters.

Answer

The lateral surface area of the cylinder is 120π square meters.