Question

which of the following is true about comparing the volume of a cylinder and a rectangular prism with the same base area? a. the rectangular prism always has greater volume. b. the shape with the smaller radius will always have more volume. c. the volumes depend on the height of each shape. d. the cylinder always has greater volume.

Explanation:

Step1: Volume formula for cylinder

Volume of a cylinder \(V_{cylinder}=B\times h_{cylinder}\), where \(B\) is the base area and \(h_{cylinder}\) is the height of the cylinder.

Step2: Volume formula for rectangular prism

Volume of a rectangular prism \(V_{prism}=B\times h_{prism}\), where \(B\) is the base area and \(h_{prism}\) is the height of the prism.

Step3: Compare the two volumes

Since \(V_{cylinder}=B\times h_{cylinder}\) and \(V_{prism}=B\times h_{prism}\), when \(B\) (base area) is the same for both, the volumes of the cylinder and the rectangular prism depend on their respective heights (\(h_{cylinder}\) and \(h_{prism}\)). If \(h_{cylinder}>h_{prism}\), \(V_{cylinder}>V_{prism}\); if \(h_{cylinder}

Answer:

C. The volumes depend on the height of each shape.