Question

determine the volume to the nearest cubic unit. if 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 formula for pyramid

The volume formula for a pyramid is $V=\frac{1}{3}Bh$, where $B$ is the base - area and $h$ is the height.

Step2: Recall volume formula for cone

The volume formula for a cone is $V = \frac{1}{3}\pi r^{2}h$, where $r$ is the radius of the base and $h$ is the height.

First part: Volume of the cone

Given $r = 6$ cm and $h=8$ cm.
Substitute into the cone - volume formula:
$V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times\pi\times6^{2}\times8$
$=\frac{1}{3}\times\pi\times36\times8$
$=96\pi\approx96\times3.14 = 301.44\approx301$ $cm^{3}$

Second part: Volume of the pyramid with the same base and height as a cube

The volume of a cube is $V_{cube}=s^{3}$, and the volume of a pyramid with the same base and height as the cube is $V_{pyramid}=\frac{1}{3}Bh$. For a cube, $B = s^{2}$ and $h = s$, so $V_{pyramid}=\frac{1}{3}V_{cube}$.
Given $V_{cube}=960$ $cm^{3}$, then $V_{pyramid}=\frac{1}{3}\times960 = 320$ $cm^{3}$

Answer:

The volume of the cone is approximately $301$ $cm^{3}$. The volume of the pyramid is $320$ $cm^{3}$.