Question

Цилиндр и конус имеют общее основание и высоту. Найдите объем конуса, если объем цилиндра равен 120 п см3 Помогите пожалуйста, это срочно ​

Answer 1

Ответ:

40п см³

Пошаговое объяснение:

V(цил.) = Sосн.*H

V(кон.) = Sосн.*H /3 = V(цил.)/3

V(кон.) = 120п /3 = 40п (см³) - объём конуса

Answer 2

Finding the Volume of a Cone

To find the volume of a cone when the volume of a cylinder with the same base and height is given, we can use the formula for the volume of a cone, which is given by:

V = (1/3)πr^2h

Where: - V is the volume of the cone - π is a mathematical constant approximately equal to 3.14159 - r is the radius of the base of the cone - h is the height of the cone

Given that the volume of the cylinder is 120π cm³, we can find the radius and height of the cone using the relationship between the volumes of the cone and the cylinder.

Calculating the Volume of the Cone

The volume of the cylinder is given by the formula:

V_cylinder = πr^2h

Where: - V_cylinder is the volume of the cylinder - π is a mathematical constant approximately equal to 3.14159 - r is the radius of the base of the cylinder - h is the height of the cylinder

We are given that the volume of the cylinder is 120π cm³. From this, we can derive the relationship between the volumes of the cone and the cylinder:

V_cone = (1/3)V_cylinder

Substituting the given volume of the cylinder, we get:

V_cone = (1/3) * 120π

Solving for V_cone:

V_cone = 40π cm³

Therefore, the volume of the cone is 40π cm³.

Conclusion

Given the volume of the cylinder, we have calculated the volume of the cone using the relationship between the volumes of the cone and the cylinder. The volume of the cone is found to be 40π cm³.