Question

a cylinder and a rectangular prism have the same height. which feature determines which shape has a greater volume?
a. height
b. circumference
c. radius
d. base area

a rectangular prism has a length of 6 inches, width of 4 inches, and height of 3 inches. what is its volume?
a. 60in³
b. 72in³
c. 54in³
d. 48in³

Explanation:

Step1: Recall volume formulas

The volume formula for a cylinder is $V_{cylinder}=\pi r^{2}h$ and for a rectangular prism is $V_{prism}=lwh = Bh$ (where $B$ is the base - area and $h$ is the height). Since they have the same height, the base - area ($B$ for prism and $\pi r^{2}$ for cylinder) determines the volume.

Step2: Calculate volume of rectangular prism

The volume formula for a rectangular prism is $V = lwh$. Given $l = 6$ inches, $w = 4$ inches and $h = 3$ inches. Then $V=6\times4\times3=72$ $in^{3}$.

Answer:

1. d. Base area
2. b. $72$ $in^{3}$