Question

a cube has a volume of 960 cm³, what would be the volume of a pyramid with the same height and base as the cube?

Explanation:

Step1: Recall volume formulas

Volume of cube $V_{cube}=s^3$ (where $s$ is side - length), and volume of pyramid $V_{pyramid}=\frac{1}{3}Bh$ (where $B$ is base - area and $h$ is height). For a cube and a pyramid with the same base and height, if the side - length of the cube is $s$, then $B = s^2$ and $h = s$ for the pyramid.

Step2: Find volume relationship

Since $V_{cube}=s^3$ and $V_{pyramid}=\frac{1}{3}s^2\times s=\frac{1}{3}s^3$, the volume of the pyramid is $\frac{1}{3}$ of the volume of the cube.

Step3: Calculate pyramid volume

Given $V_{cube}=960\ cm^3$, then $V_{pyramid}=\frac{1}{3}\times V_{cube}$.
$V_{pyramid}=\frac{1}{3}\times960 = 320\ cm^3$

Answer:

$320\ cm^3$