Question

The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the cone to the volume of the prism?

Answer 1

Answer:

1/3

Step-by-step explanation:

The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the cone to the volume of the prism?

Cone Base Area = B = π R²

Cone Volume = (1/3) π R² * Height

=> Cone Volume = (1/3) B * h

Prism Base Area = B = Length * Width

Prism Volume = Length & Width * Height

=> Prism Volume =  B h

volume of the cone / volume of the prism   = (1/3) B * h / B h

=> volume of the cone / volume of the prism   = 1/3

ratio of the volume of the cone to the volume of the prism = 1/3