Answer:
The height of the cone would need to be approximately 2.29 cm if it has the same volume and radius as the given cylinder.
Explanation:
The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the cylinder and h is its height.
For this cylinder, the volume is:
V_cylinder = π(5 cm)^2(12 cm) = 300π cm^3
The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the cone and h is its height.
For a cone with the same radius as the cylinder, the volume would also be 300π cm^3. Therefore, we can set the volume formulas of the cylinder and the cone equal to each other and solve for h:
V_cylinder = V_cone
π(5 cm)^2(12 cm) = (1/3)π(5 cm)^2h
Simplifying this equation, we get:
60 cm^3 = (1/3)(25π)h
180 = 25πh
h = 180 / (25π)
h ≈ 2.29 cm (rounded to two decimal places)
Therefore, the height of the cone would need to be approximately 2.29 cm if it has the same volume and radius as the given cylinder.