Question

Площадь осевого сечения цилиндра равна 30 см^2, а площадь основания -9пи см^2.найти объем цилиндра

Answer 1

9пи=пи×R²
R²=9, R = 3 см - это радиус цилиндра, выраженный из площади основания. Диаметр цилиндра тогда равен 6 см (D = 2R), высоту найдем, поделив площадь осевого сечения на диаметр:
H = 30 см² : 6 см = 5 см.
Объем найдем, умножив высоту на площадь основания:
V = 9×пи×5 = 45×пи ≈ 141,37 см³

Answer 2

Calculation of Cylinder Volume

To find the volume of a cylinder, we need to know the area of the base and the height of the cylinder. In this case, we are given that the area of the base (A) is -9π cm^2 and the area of the cross-section (A') is 30 cm^2.

The formula to calculate the volume of a cylinder is:

V = A * h

where V is the volume, A is the area of the base, and h is the height of the cylinder.

To find the volume, we need to determine the height of the cylinder. We can do this by dividing the area of the cross-section by the area of the base:

h = A' / A

Substituting the given values:

h = 30 cm^2 / (-9π cm^2)

Now, let's calculate the height:

h ≈ -3.35 cm (rounded to two decimal places)

Finally, we can substitute the values of A and h into the volume formula to find the volume of the cylinder:

V = (-9π cm^2) * (-3.35 cm)

V ≈ 95.03 cm^3 (rounded to two decimal places)

Therefore, the volume of the cylinder is approximately 95.03 cm^3.