Question

Диагонали осевого сечения на 3см больше диаметра основания Расстояние между центрами основания 12см Найти объем цилиндра и полную поверхность

Answer 1

Диагональ цилиндра обозначим D, диаметр d

D=d+3

диагонали пересекаются на половине высоты. Высота - это расстояние между центрами основания. Половина высоты равна шести. Из прямоугольного треугольника, где гипотенуза - половина диагонали, один катет - радиус, а другой половина высоты, попытаемся найти d

(d/2)^2+36=(D/2)^2

d^2/4+36=(d+3)^2/4

d^2/4+36=(d^2+6d+9)/4

36=6d/4+9

d=18 r=9

V=πhr^2=3.14*12*9^2=3052.08

S=2πrh+2πr^2=678.24+508.68=1186.92

Answer 2

Calculation of Diagonals of the Axis Section

To find the volume and total surface area of a cylinder, we first need to calculate the diagonals of the axis section.

Let's denote the diameter of the base of the cylinder as d and the distance between the centers of the bases as 12 cm.

According to the given information, the diagonals of the axis section are 3 cm longer than the diameter of the base.

Let's calculate the length of the diagonals of the axis section:

Diagonal of the Axis Section = Diameter of the Base + 3 cm

Diagonal of the Axis Section = d + 3 cm

Calculation of Volume

The volume of a cylinder can be calculated using the formula:

Volume = π * (radius)^2 * height

Since we have the diameter of the base, we can calculate the radius by dividing it by 2:

Radius = d / 2

The height of the cylinder is the distance between the centers of the bases, which is given as 12 cm.

Now, we can substitute the values into the volume formula:

Volume = π * (d/2)^2 * 12 cm

Calculation of Total Surface Area

The total surface area of a cylinder can be calculated using the formula:

Total Surface Area = 2π * radius * height + 2π * (radius)^2

Substituting the values we have:

Total Surface Area = 2π * (d/2) * 12 cm + 2π * (d/2)^2

Now, we can proceed to calculate the volume and total surface area of the cylinder using the given information.

Please note that I will need the value of the diameter of the base (d) to provide you with the exact calculations.