The cone is inscribed in a cylinder whose height is 20 cm. Find the volume of the cone

The cone is inscribed in a cylinder whose height is 20 cm. Find the volume of the cone if the volume of the cylinder is 36 cm ^ 3.

1. According to the problem statement, the cone is inscribed in the cylinder, which means that they both have a common base and common height.
2. When calculating, we will use the formulas:
a) the volume of the cone V con is equal to 1/3 of the product of the base area by the height;
b) the volume of the cylinder V cyl is equal to the product of the base area by the height.
V end = 1/3 P * R² * h, V cyl = P * R² * h, and therefore
V end: V cyl = 1/3 P R² h: P R² h = 1/3.
If it is known that V cyl = 36 cm³, then V end = 1/3 * 36 cm³ = 12 cm³.
Answer: The volume of the inscribed cone is 12 cm³.