To determine the relationship between the volumes of the right triangular prism and the right cylinder, we can use the formulas for their volumes.
-
Volume of the triangular prism (V_tr prism): \[ V_{tr , prism} = \text{Base Area} \times \text{Height} \] Since the base area is a right triangle and is congruent to the base area of the cylinder, we'll denote the base area of both shapes as \(A\). \[ V_{tr , prism} = A \times 6 \]
-
Volume of the cylinder (V_cylinder): \[ V_{cylinder} = \text{Base Area} \times \text{Height} \] The base area of the cylinder is also \(A\). \[ V_{cylinder} = A \times 6 \]
Since both shapes have the same base area and height, we can equate their volumes: \[ V_{tr , prism} = A \times 6 \] \[ V_{cylinder} = A \times 6 \]
Hence, \(V_{tr , prism} = V_{cylinder}\).
So, the conclusion that can be made from the given information is:
The volume of the triangular prism is equal to the volume of the cylinder.
1 answer