Question

Fruit juice comes in two types of containers. The first is a rectangular prism that is 9 inches tall and has a rectangular base that measures 2 inches by 3 inches. The second container is a cylinder that is 8 inches tall and has a radius of 1.5 inches. Which of the following statements is valid? A. The volumes are the same. B. The prism has the greater volume. C. The cylinder has the greater volume. D. The volumes cannot be determined.

Answer 1

The volume of a rectangular prism:

`V_p=Bh\\\\B=wl\\\\w=2\ in;\ l=3\ in;\ h=9\ in`

substitute

`V_p=2\cdot3\cdot9=54\ in^3`

The volume of a cylinder:

`V_c=\pi r^2h\\\\r=1.5\ in;\ h=8\ in`

substitute:

`V_c=\pi\cdot(1.5)^2\cdot8=\pi\cdot2.25\cdot8=18\pi\ in^3\approx18\cdot3.14=56.52\ in^3`

Answer: C. The cylinder has the greater volume.