Question

Цилиндр и конус имеют общее основание и общую высоту. Вычислите объем конуса если объем цилиндра равен 87

Answer 1

Объём конуса равен 1/3 × S × h (S - площадь основания)
Объём цилиндра - S × h.
Стало быть, объём конуса = 87 / 3 = 29

Answer 2

Calculating the Volume of a Cone

To calculate the volume of a cone when the volume of a cylinder is given, we can use the formula for the volume of a cone, which is given by the equation:

V = (1/3) * π * r^2 * h

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 87, we can use this information to calculate the volume of the cone.

Calculation

The volume of the cylinder is given by the formula:

V_cylinder = π * r^2 * h_cylinder

Where: - V_cylinder is the volume of the cylinder - r is the radius of the base of the cylinder - h_cylinder is the height of the cylinder

We are not given the specific values for the radius and height of the cylinder, so we cannot directly calculate the volume of the cone using these values. However, we can use the relationship between the volumes of a cone and a cylinder to calculate the volume of the cone.

The relationship between the volumes of a cone and a cylinder with the same base and height is:

V_cone = (1/3) * V_cylinder

Using this relationship, we can calculate the volume of the cone using the given volume of the cylinder.

Conclusion

Without the specific values for the radius and height of the cylinder, we are unable to directly calculate the volume of the cone. However, we can use the relationship between the volumes of a cone and a cylinder to determine that the volume of the cone is one-third of the volume of the cylinder. Therefore, the volume of the cone would be one-third of 87, which is approximately 29.

So, the volume of the cone would be approximately 29.